IM Geo.6.2 Lesson: Transformations as Functions

Mentally find the coordinates of the image of A under each transformation.
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gFvjsbTADRePj1zOaaTIYBBA29s+br0BqHxMlNh5syZHY3UrY9/byUNnx8bo7/xjW80dQ6qFI13jz328MknuaaeAC+DgCnNVCIbaQQvbZlOJmniS54YvtAcJPBKHdz2hOLc9CZhaKJgsmAsBf1QnfoCL28CcbErFaIHCIrGG0qXusTy/SXDseiW0UFrybVkGBm6Gm8OmdL20JJhXyaAFoNw1I968fWBLXqttdYyRx55pJ+99FqAt98CilIiNRMFeFOZGqiOf79cjddPq1n9StkHCbxSwRztFFNDDl60S4DX5ddl4+VN4CaKMFL5aLwCvKl4uHQFeHMt+4R3TuCFHyvXmMebcwEFGq87uBbqQ5wmzDLhbbbZxrz1rW81W221lV3J9tvf/tbUXdAyCOCVBRQ5NV4XeN1+nCrMc7Eq704mcnNXrklcSl+A1+XRAd5B7dUwCODNaWoQ4A2BkXsjYoXF1JATeN0lw0XtQOaMYDPtjPm7bKrD9KUmbhDAi0mM3clSary+LHID71DQeH0ZpLgWjTcF7RBNF3gFBzrAq/vxhkTWPk6Atz2lahTcvRqqlWifqwrwtufyIoVBAK8/uPZibdKFFHjTyHaQwCstUuAVSSTyFXjjC1aBN75Moagabxq5uhqvcFDgFUkk8hV44wtWgTe+TKGowJtGrgq8f/7zwPbjTXNLe6mqqaFXJjFi1NQQQ4q9NFaHBRQKvAq8vT0/QozaeCMIMUBCbbwBoUSIUhuvM483gjz7kpDpZHxS5XJqaogvaTU1xJcpFNXUkEauqvGqxpukZ6nGm0SsXSdQpOHQTVWBt1sesa4UeBV4Y/WlLjoKvF3iiHahpoZoouwipKYGNTV0dYgYFzq4FkOKvTR0cK1XJjFidHDtrrsGcsowangupzbeNJJWjTeNXFXjTSNX1XhV443es1TjjS5SS1A13jRyVY1XNd4kPUtnNcQXq85qiC9TKOrgWhq56uCaDq4l6VlqakgiVp3VkEas2Y93V+BV4E3SlRV4k4hVgTeNWBV43Y3QE8m4i6wOrnWJI9qFAm80UXYR0sG1LnFEu9DBNR1ci9aZhJAOrokk4vo6uBZXnkJNB9cGMLjGWfO5p5PlPnNNB9fkEWvvyybSgxhc043Q29+/EAUFXgd4pYOHBNUkzqXnhuXoH4kTvwmPfmWgPZRMDanaisbLWWY5T6Coe8pwv3tVlo7cyoA3lVxF40159I/fbt/UkKptwpejf8aPH2+Pj5K41H4R8KZsK6aGIXXK8NSpU1PLuYs+2icdOpd7/PHH7SnDOR8eTooFKHK5Z5991gJvnVN729bt9ttv7zpzrS29fuU5QmiNNdYwOQ+7XLFihT22KCUg+O2m71x55ZV+dLJrnouzzjrL0IdyOe4lQJjLcf84W3LJkiW5WBrO6wPrXNfZCJ03wIQJE+w5WPfdd5+59957DX6KH7Q5b2vcuHEWlAin4OPShAeHMsIToZOWqo1CF54crIfm4rdR8rh1bBuGB2fnnXLKKQYt1OfZln6oPDwAB04RXrZsWXSZ0i/lx33jd9FFF1ng3WWXXczSpUs76eQj/Z577onWn6Sv8vJEG+Q6xb0T2co9wwcg+BHOwRNZjh492vYhqYfUK5U/d+5cizs+/RTthSbtAuf+9Kc/ZXs+brrpJrsPeBB4Efqxxx5r33icNMqPt5+EY/rQ5Qc/TsRNxcetM8IeO3asOeaYY+wD5KbFCEubhBbX8DzhhBMsEHLNgyvpKXx48GLhuHTMDVyn4OPShMfIkSNtO11+hN1rt0ydMO0YNWpU58f1IYccYoH3fe97n20vYOH+RM4x+FNX6Jx++ulm2LBhXfKMRT8kD2jTd0466STbj8gj7ZI6hcq1iYP+0UcfbWWasm1uHVESXLkKX/HdvDHC0IUfB67yfMagWUYDfvAij+s6Gi+HXaKdsXol5Y+jvIU+6jdvILl209ywpLfxobd8+XIzadIk8/TTT1uesXn49cNmNnv2bLNgwYIs/OCPOYWXGZ/Gfn1SXd9yyy1mxowZXW2MJduVK1ca/zd//nwLvLvvvrs9Gt5Pj8Vb5AW9Bx54wDAmAS/iY/MQXkIb+vQdzA30o5T8hP4zzzxjwZ0+5NYnZfjGG2+0Jhzh4bbTDUt6Gx96tJWTrhcvXpytjWBcoalhUKcMM1pc5GLb0xhwYiYFNy+Xw8zAp0ZqJ7LipYJ29thjjxmJS80bs8asWbNSs+nQZ0AGG+9ee+0VbGOKdmOnk+PdU9DvNM4J0Hf4FMfBMwVflybPBRoafSiX415OmTKli51bp66ESBe5B9fAOHDHdV0aL/aklM4XKG+BXNPJ4D2UZjWkknPuebzINfWsBr/flM1qSCVXBoGxYz///POpWPTQ9Wc19GSIHAHw8klMH8rluJc+8KbmrQsoMgIvN1OBN02X1pVraeS6OgBv0XSyNBL9K1UFXgXe6P0rt8ZLAxR4o99GS1CBN41cFXgVeKP3LAXe6CK1BGUBhZoa4spXNV5n5Vpc0RZTy2njpRZqaii+F21SVONtI73isqrxFsumTYpqvKrxtuk/wbKq8QbF0jpSNd7WIgwSUI1XNd5gx2gbidbCXMVcToE3jaQVeNPIVYFXgTdJz1LgjS/WQU0nk3m88VsUpqimhrBc2saqqUFNDW37UE951Xh7RBIlQjXeKGLsIaIar2q8PZ0iRoRqvDGk2E1DNd5uecS6GsQCCgVeBd5Y/beLjgJvlziiXCjwRhFjDxEF3h6RRInQwy71sMsoHcknotPJfInEuVYbbxw5+lTUxqs2Xr9PtL5WG29rEQYJqI03KJbWkWpqUFND604UIqCmhpBU2sWpqaGd/IpKq6mhSDLt4tXUoKaGdj2ooLSaGgoE0zJaTQ0tBVhQXE0Namoo6BrNo9XU0Fx2ZSXV1FAmneZpampQU0Pz3lNSUk0NJcJpmKSmhoaC61NMTQ19BNQwWU0Nampo2HXKi6mpoVw+TVMvvfTSzgkUIRr+BvGhPFXjoMXROLIRekzaZXVQjVc13rL+0ThtUBovR//kcm2A133AJSx+Uf1F4+Xon9RO6jIIUwPAe/nll6duYoc+Gi9H/2CuyuUGBbycSJ3LcfTPkDtzLdfRPwh5UGeureqb5Nx6661m5syZffuxgJj4fQsUZBDg3XPPPQtyxI2mvoMA3tVhcI17ySG7OR2Da3feeWc2lmpqUFNDks4mh11WAVQ+ZznFlt8LL7xg6yPlxO9XydzAS30UePvdlWbpN998c1bgpY8BvDk1XgFet39nPezSvzWrw0boHM+d85RhmdUw1EwN9913n/nDH/5gPvCBD5hNN93U/j73uc+ZSy65xO8WnWu3o3YijTF8nsopw258irDUQYE3hXSNGZTGy6nqudyQNDU8+OCDudpvT6CYNGmSHUTIxTS3jfepp56yx7tjVsnlqth4f/jDH5p3vvOd5thjjzUzZsywJ8vuuOOO5lWvepWZN29eraoOUuMVLb1WhRtmzm1qkME1+lAuF7LxyssuVR10Hu855xjeBqkFLTdQjv557rnnJCq5nxt4RePNBbzcO4B31qxZpbJEA/cHbZ588knzpje9yXz7298uLesnDhJ4c565xtfSFVdc4Tc/+rU8fzKd7Omnn47Oo4hgCHiL8saKv/DCC81qr/GuWLEiljz70uFBP/fcc/vmi5lh7ty59nMqJs0yWmgtY8aMMbQ1l7vjjjt6TAbyMPerA1rwd77znX7Zul7OixYtsqaGvffeu2+5WBkeffRRq6XHoldEB7mJ7ObMmWOuvPJKm9WNl7KST65j+MxqAIBzuVtuucUAhDnd1KlTzT333JONJRhXOKthyZIlZsSIEQYNjTctfuof/BBCDn7wuOiii8xJJ51kZs+enbxtIjtAcOLEiUF+TBeSfG186IgMmV0wfPhw+znfhmadsrzMRo8e3amDX5a6UUeA5Nprr7U/AAWbL7baAw880Kb55bjmXmEHxucHnVNOOcWW+4d/+AcrPzedcIhO2zj6Kf3VvWci87a0i8rTd8aOHZukPSGeyPeEE06wM1RIT90+eGD643669REZN+EvZV16fnjkyJFm8uTJXTz9PE2vpa9Lea6ZtQEGuK4zuLZ06VJrG2Qg6IYbbrC/66+/vhOWuLa+S3PUqFH2gWO6lU/XzeenNb3mYT/11FPNggULkrXPrRvtQuDYlJCr26ZQm92ydcIu3T/96U/24bnqqqt6ZFqHZtW8tIsX2vjx4+3Zcm45t17EA4qf//znzUc/+lHzxje+0bztbW+zwILWI/JwyxB3zTXXWK2P9vC7+uqrbRkA+1Of+pRNlzR87jE0hJ5bn6ZhaPHlwsvFrV9Ten45oSk+6fCcMGGCOfvss4NtcfP69OpcCx18ngtAkD7UhIaUEZpyXeTTRl5op59+ei1+RfSqxMOTFxqmMcJVykgeaZf4xLthyYcvtPEBX14wrusALzaPadOmdT5z3EypwmhKy5cvz8bziSee6FH5U7UNunwKouVhx0rxWRiq+8qVK23Hoq05HO1avHhxj6khxJt7/dWvftUwqPahD33IAu8BBxxg+IwPOZGZ+JIHoF5zzTXN1772NYmyvuTDl3BXhhYXjzzyiDU1xKZbVCX40HcYeBSe4heVaRsPfUwN9KEmrm79yL9w4cKXlKmhbhuRI32n0NQA8IqtRYjjp/pRISrD4BrO5SnXMXi7tGRwTWxYMekLH3yctIdPDn86maRJvjb18GkwgMUbncG1NnSrloW/P6tB2ic0yCNO4rgHDJJtvfXWhhVozBaQNMlb5Mvg2h577NGTRXiTIPTa+MJAppP5sxra0Ja6FvloSmja0hbXl3Bb/lIeejK4Rh+S+H4+5Vwn8qGcOAmLT7yE3Xm8xDX5CT0pK3zFZzCdAcNnnnnGRjGrRgbXpEw/X2jhk/fZZ581zP6Q9ko6ab5j5hZfLq7r0ngB3lBBt0DMsMzjzcXTB96YbQnRol3YnPj0yNVGHprTTjvNAm+oTrHjaJcLvEXtLIo/7LDDzIYbbmhCKxiLyvAiK5vHS7misk3aDy2A97zzzjO5ZsTAk77DkuGYbSlrvwu8ZflCacjmG9/4hrn44osr15d2xZrVgJnp61//emcgG9qYAfbff3/zwQ9+0LzhDW8wb37zm83uu+9ufvrTnxrmldeVK/kxG6IovOUtbzGve93rzEc+8hFzzDHHGL4wXXrHHXec5Q3YP/zww12D+uTrAV5XqGSI8YOm0JEwvgCvG0c+/1rKtvUFeBn5d/m0oevX1VbeeaOj8WLncZ3wk7Jy3cR3aRAGeLGZyQKKJjTrlIGnC7xSH3yc0PrbZY/3u9/9zmy88cZB4O3J/LcI0XhZMgz9Mif82/jQF43XnU7WhqZbFvpyLWF8+o7s1SDp+JLHjWsTtgT/pvFiqxeNtyofTEhbbbWVfRnut99+XfUTGq7vhl3gddtmiThyKWsfzzVjBttvv70FQMoySIg5ir7Fl9Hvf/9787Of/cy8/vWvt/U85JBDLIsyulIfMvI87brrrrbsu971LvPjH//Y0Hc//elP27gvfelLVgOWMgxUohwcccQRdv1AJVODNDqmLxVyaYqpIZTm5osVFuAVU0MsumV0QsBblr9NGnLkk2qQGm+o/tSJlw+fZu69BrC33HJLs9tuu4WKFcYBvDxUPvC6tAsLN0wIAW9DUpWLCfCmbJdbmaYa729+8xuz1lprmU022cR88Ytf7LrHLv1QGOCdMmVKKKly3KGHHmpBTswyFGRQ9qijjrIvTJcQpk2Ac9111+2YG9z0ojCy+ed//mdrxnNt4HwBAeiArD9zgemOr3nNa6y5yN+Pwmq83FjXxlvEPHa8q/HGph2iN1SAN+WDhLYiNt6QDFLE+Rqvz4PBM7QR7Lk77bSTBdpPfvKTVhv5xCc+YT/7/DLutS8vV+N186UMDxJ4U7bLpS3AW2cBBfNh119/fbPPPvvYQdN3vOMdteYBtx1cY47s5ptvbj/5fXur2/JlfJUAACAASURBVDY3jPkBoGTwMoZjk6iXv/zl5gc/+EEXOWbYwAcTjIyfSYZSU4NkSuWvrsCbSp7QFVNDrpVr8OwHvAAnm5KMGzfO/Pa3vzU/+tGPrDbC9DJXe6gqFwXeqpKql0+Alz5U1QE266yzjrn99tvNN7/5TavhsQFSP4ftk9F+VuadccYZNsy1+0NR8l+6Pl3m4wJuJ598sp9UeP3973/flrnuuusK89RJYAHR2muvbcTMImVpIwuENthgAzvdUuLxFXhdaSQI5zQ1UP2hCLxVxdrvIRM6Crwiibh+CHjL7gnmIwCHT20cPiYgpheGnEuLwScA+5WvfKWlQdj/vf3tb+8azHTLC/19993X8mRhThVH39lss83sgFusPSnOP/98C+TMu/YdLyZeDEceeWRXkgJvlzjiXyjw9pdp6IEqK6XAWyad5mkh4C2ixmc9A0qvfvWrDateccOGDbMgIwOCbln/HqMhs6gAQGIuN9OtuMaX8PTp00s1XgbJmbGAbVmmT7o8CfNyABhPPPFEw0ZN22yzjdVC58+fX0rbp1N0jaKzww47WDNaaPsDTvQAeBmMw4kcFHiLJBopXoG3niClY5aVUuAtk07ztCLgde+JhOnXAMrhhx/eYcgAEhqvP2dVMkhZriWMdly2ib7kExquj1mCWQrvec973OiuMLZnBtLQrKkvsx/YG6RIK+8qXOHi4IMPtnTdWQtSZ3xWWsIXM4zEQ1aBt4Jw22RR4P2r9NxOV0WeZfkVeKtIsH6eIuD1KZGPZd8MKLEEn4Ejlv7+8Y9/tCCD5tvPoa2ykRPLk5kNQNj9MS+2nymAGQrYTz/zmc8UsiMPEwfQsJkXjXYNCLNysu6WtPRJ+cGQ+buA6kEHHWT5S58Vn0hmbbzsZS+zXwduJRV4XWkkCCvwxheqAm98mUKxKvCi0QI4oR8aLwsUcC4A+TVmTwhsrZgJAM8tttii58em+dSpyLHoZr311rP7fxTlceOlPgAldWfxThMHHTbagQZTzNzZFMJDfJnxgFnGdQq8rjQShBV44wtVgTe+TKFYBXjRRLfbbju7YAKbLPZT9lxh5RqLLwBR5vK6YARtASLxWVXGLnoMyLEfM1oyA274xPNjIZBLR8pK65nit9FGGxl2qavqoIHdlRfELrvsUrVYVz72s3jFK15h687SYXF+/YjHlgxAs0eJ6xR4XWkkCCvwxheqAm98mUKxCvAef/zxFkiYGhhy733ve822225bqqm65ZiKxTLjJo7VZCwDxm7rrijsR4utNgHD0F4f/coCuszkQNMNAa1fXlawffe73+1KUuDtEkf8CwXe+DJV4I0vUyj2A16WBrM/AcAamuuLdrrzzjvbz/8qc3nh6S4ZbtKqz372s/b4KNn0RtpBXX0nQClTvNjmE0c8m/Vgsy078QPQZbEI+0gXOeEh6SwZBuTFDizxCrwiiUS+Am98wSrwxpcpFMuAF0D51a9+ZUEEs0KRYxYBQMNgVhXXFnhluTB7QovDHPL+97/ffOELX7DT1agvy5KxKxNH/Tho1X05yOwEDkoIOQYBWRaNTZkFQNixf/KTn3T5TBnz2405g8E19o5wnQKvK40EYQXe+EJV4I0vUyiWAS8zANi4HsAqW22IKYKBsqoLGtoCL7ZigBQwFEc7AFDqy2Gq/FicAWgSh4mB1ZaineKzlJ18RdPM2KucpcmckI3Wy/xl9mHgB13x3WXIy5Yts8viWUYtLyvhqcArdyuRr8AbX7AKvPFlCsUy4JU9bf1tMQVIpEakM+BU1ebaFniZlvbxj3/cbi0qe3tLXWgPMx/YD4KtRNkKkjgWZrCEXRy2YuzEbNBf5DCj0C6WARf92OPCHQwE/HkpcLK27tVw9tlW+EUCjh2vwBtbosbuuUqHZneyXG512iTHt98KuIrfT+ZV80GnLfBCg2eMWQps04hz+bthSZPj3SWNOtCfmKERcuSTvJLuX/vx7DPBwB8r6zhWzT9kVzVekVgiX4E3vmBV440vUyiWabz9OBYBUb9yMYAX3thXmRPs21hd/lJHAV5JY2CNATNsw3Wd0KSchPGZI8xewJxjx+587so28irw1pV0zfwKvDUFViG7Am8FITXI0gZ4G7CzRWIAL4TQ0jmFAtMCwCcgGKqXD7yhPG3iMLNw6gx2ZBx1UuBVU0ObPhUs229byGChFpEKvC2EV1L0pQy8Jc3qSUoNvD7oDzngxe5BpXK5obIResr28uZnxU/O/XhZFlm20Ums9kqHljPXQhPgJU8snkKHgRtsgFUHjaRcVT9Ub76WQjt9VaVZNx9tY2tDBo9yOfewy1w8UwOv345S4GWUzx958wnEvu63EXqoM7apw6oMvCKrQQBvTo2XdspgiD+4JjJo00eKyq4Og2sALiPx2CRzOe4lQJjT5QZepuIVmhruvPNOC7wpO68rXPj4wJuatw+8MfhBo4wOWgv2HnH98ku+Jj60BwG8t912m9V4XTm44SZtKSsjpoaQxltWrmkabUkJvEWyklOGpd5F+SS9qQ9dvj4/9rGP2fmp73vf++xigyLtPmY9AF4WN7g03XDTNkk5aPn02L7SXekmeVP48C4FXirC1m45HcBLhw45X1ihPHXjmK/Hxh7YsnI5JlTzaZzLMZfQPWU4B99Babwcs+32Ezccu90c0Y2pwZ2nGZuHT4++U7aE1c/f9JrJ/Uyn8n9sHu672DIelKnBncfrtzH2NWYq0XhFfl2zGji/CI2JH3thSjiGDyD4dABBdq9Pwc/nxfUDDzxg9/5k2kgoPUUcG4CwiicF7RBNdsFnDTp2pVB6ijg0UCalQzt2v4Ee94u9WvG5ls2l2fGJeOL4SVjaSJyE2/oc6sjDwzLTtrSqlqfvoPWG8sdqGzJF0wV0mQvrgi+LCtjzwOUfi6/QZPcugJ9rl7YblrxtfaEJv0WLFnXxa0u7rDwYJ8AroN4BXib5cgwH2lLKH0ePC32OX2ZfS7lO4XPirtBl0+ajjz7aHn8ucW19tz0hWmxvh93MrUcoX6y4UaNGGTbmwI9Fsx8d2sfqnBRtpH+wxl5+tOvAAw+0AMHJxchf0sSP3XbaRT3YRMW93ynaK7KGNn2HrRJT8oEHWxy6gCthgJj5qOxERr1oe+y6oFUjV2l3Sl/qTl8dMWJEFp60h4M42WDHdR3gRfXGzsMbHVsoo+KxfiF6fPZTGbaFIyy83LDEtfGFHv69995r9+JEK5T4NrTLykKf34wZM+z8QuQq+UPykLQ2PvzQdHnBsDwydRupKzxYL8/AbAp+0HR/aGgcmw0ofOUrX7Farpueog60kzEQvtAYeErFAz7SN+BB35k1a5Z9Jtv0i7KymFDYyjGk8W699db2mfHb61+X0e+XxuYz8iXRL2+TdOQpMqU8/Qecw7Ycsx1FdYMH+z/4xyGtITYHbLxsBCHXLjqnCMMHAfjrq1PwEpqAHwIoGjSQfDH9yy67bCA2XtqayzG4BkC4LmU/klkN2HhTO2kHAIUpTq5T8HVpE6bv5LDxogCJluv6/sm4KdqMjTf3rAbGsgZl4xUZdjRegHeoTSeTSsbyefMBvDkH13TlWqy79yIdmdXgTyd7MUf8UMpZDUW1zTWPF0UEUwq7aLGL15ZbbmnNVdhEUzteoswyyOlyTycrncerwJvm1ivwxperAm98mUKRz2UOrGT6k6t9p+H2V6oKvKrxJulfCrzxxarAG1+mUETz5cTfnCvXFHgVeJP0ZgXe+GJV4I0vUyhigsPey9TPXE6BV4E3SV9T4I0vVgXe+DKFomySk8O2Ky1Q4FXglb4Q1VfgjSpOS0yBN75MoSjAy2IAXA47rwKvAm+S3qzAG1+sCrzxZQpFH3jTcOmmqsCrwNvdIyJdKfBGEqRDRoHXEUbEoAJvRGE6pHQ6mc7jdbpDvGDOTXKotQJvvHvnUlLgdaURL6zAq8Abrzc5lBR4HWFEDPK1lHMjdAXeiDfPIaXAq8DrdId4QQXeeLJ0KSnwutKIF9aVa+eco0f/xOtPlhIj0uyIxCqkXE6BN42kFXjTyFWBV4E3es9S4I0uUktwVd6rQSSmpgaRRFxfTQ1qaojbo/5GTTXeJGI1qvGmkatqvKrxRu9ZqvFGF6klqBpvGrnqPF6dx5ukZ6G13HjjjUloh4gq8Iak0j5Ogbe9DEMUFHgVeEP9onWcAm+3CFmG2nYpqs7j7ZZprCu18caSZDcdtfGqjbe7R0S6qmLjbQu2blUVeF1pxAsr8MaTpUtJgVeB1+0P0cJVgFeYxQBgBV6RZlxfgTeuPIWaAq8Cr/SFqH4d4IVxW/BV4I16+zrEFHg7oogaUOBV4I3aoYRYXeClXBvwVeAVycf1FXjjylOoKfAq8EpfiOrXBV5meRx88MHm/vvvb1QPBd5GYutbSIG3r4gaZVDgVeBt1HH6FaoDvBwts/HGG9vjxK+77rp+pIPpCrxBsbSOVOBtLcIgAQVeBd5gx2gb2Q94MSs8++yzZv/99zebbLKJOfTQQ80WW2xhFHjLJa8r18rl0zR1SK1cu/POO83UqVObtqVRufPOO88sX768UdkmhR5//HFzzjnndOyLbeyMVfnPmTPH7h/r50/FG4AbM2aMeeKJJ3yWya5vv/12M2vWrFL6K1euNPvtt5+55ppr7PHhm222mbn++utLyxQlLly40GrMe++9d1GW6PErVqwwkydPjk63jCB9Z968eWVZoqbRJydMmGBfklEJlxDjXgKErkv1bAiPCy+80CxdulQuk/sPP/ywxR2X0Rpycdddd5lx48YZHiI0mNtuu836hNv+hJb4Qp9dtHgQ5dr12/KU8sITnwcdnrfcckvU9vm83Hace+655qKLLgryk7pJ+bY+9PgMP+mkk8wNN9wQ5NmWh1+e/oJmNmnSJMsv1CbiFi9ebHi5L1myxMycOdNssMEGtjPecccdnf5FPikvPvQlHp/8F1xwgVlzzTXNTjvtZK/ddLd+QsONaxKGzrXXXmtfaLfeemunPk1ohcqE6kkcfQewl2eSssTLL0SrTdyiRYvMyJEjDavJUvCAptRPwhdffLE544wzLD+3fZKvrS98hA6yhN/cuXM7PCUthQ//q6++2kycOFGg1vod4OWB4IG95JJL7IPBw5Hih6Chi3/iiSeaKVOmJOETqjsPLDxnzJiRnCcaIL/Ro0eb8ePH23CoTm3j4OHSmDZtmhk2bJjhre7GpwrTX+hUp556aiV+s2fPtjJ57Wtfa4YPH24uvfTSTjm3LRKmPdw3tCLaxDXl1lhjDfORj3zETJ8+vZNGHn686KSftW039eAHAPJ8xKLbr17wPO200yzYFz2TIqN+tKqk0y6ei+OOO87KuEqZNnlErtj8kWsbWv3KunJClieffLI5++yzk2Od1Isve54RV5PvAK+YGtzELohOcMEbnTXwORztck0NOdoJj8suu8zcdNNNXUJPyds1NaTkI/cMHmgRdO6q/Pi62nTTTc2CBQsql3H5oZEBvGJqgK/7k7wxfUxi559/fhfJqu3tKlRw4dPimr7DCRR+WgGJ1tEvvPCCNTVgFsrhaJdrasjVTkyqKJq5+IFxAL3rOsB79913W43CTUwdxt7KiF8u9+e/Da795S9/ycXSfobLJjk5bvRTTz1lNaVBb4Re1lbMBQBv08E1Ad4999wz23186KGHrNb7/PPPZ+M5iME1vs7YaCmXK9skp6wPtakfX1C8/HM5MA4l03Ud4KUifMrlcCJQgPfBBx/sYSnpPQktIqApwMu0GVwMPtAoo4PWAvBKHvFbNKW0KA8Ng2u5gJf2YBtzNV5po+9Lxfm6EuCVPJJW5kteviCw8frAS7rkKaPTJA2thU9GAd5UvKT++AK8qXghB5c2zwWf/jGB16UfkrsLvOSVOoXytokT2tAA53IDL1jnuh7gdSvoZkwRFo1XeIqfghc0feCNwUfqjC9hly4Pj6/xhvK5ZdqEn3766ewaLwMI2LNcF2qjxJVpvJLHpeWHi+bxVinr06p6nUPj9evPS/uKK66oWsXW+VLM45U24UvYragLvG58yjDjAABvqD4p+JbO40ULyaXxSuMAXjp0SucKNwXw9qu7aLx+Prdeflqb60Hsx8tIvw+8ZW0oA96ycpJWBLySnsJfXfbjja3x9rsX3Es+/XGpngm/DgK8fnyqawFet309Gm8q5iG6ovGG0lLEDQJ4XY03RZt8moMAXkwNdYCXqWXrr7++naLl17/KtQJvFSnVz5NC4+1Xi0FqvP3qFitdgNelp8DrSiNBWIG3V6h0xH322cfOwe1N7R+jwNtfRk1yKPA2kVr/Mgq8umS4fy9pkKOuxiss3E8viaviK/BWkVL9PAq89WVWpYQCrwJvlX5SO09d4G0KuFIxBV6RRFxfgTeuPIWaAq8Cr/SFqH5d4G3LXIG3rQTD5RV4w3JpG6vAq8Dbtg8FyyvwBsXSOlLm8bYmVJGAAm9FQdXMpsCrwFuzy1TLXga8bc0KoRqoxhuSSvs4Bd72MgxRUOBV4A31i9ZxZcDbmniAgAJvQCgRohR4IwgxQEKBV4E30C3aRynwtpdhiIKaGkJSaR83qAUUbs11Hq8rjQRhnccbX6iq8caXKRRV400jV9V4VeNN0rNU400i1s4mOWmo91JV4O2VSYwYBV4F3hj9qIeGAm+PSKJEqKkhihh7iKipYUD78fJmz+XU1BBf0mpqiC9TKKrGm0auqvGqxpukZ6nGm0SsampII1Z7PNSQ2483UVuDZHV3sqBYWkW+FHYna9VAY+yBnhz942+E3pZuWfnVZVvIM888M+pG6GUyJU13J8t4AoXcDAVekUQ8X4E3nixdSgq8rjTihRV477rLHm0ST6QvUipavcTbNfVG6NRC+GNr4WhnDoTM5ThFl6PBczjayZlrnPj72GOP5WBpeXDYJaf/pnRyD+HB0T+5Nd4HHnjAHkcvR/+kbKvQpu/w850rCz+t6TU0OYvw9NNPN5xikstdf/31PQdBpubNyeb02Vxu2bJl9hBRl19nHi8nUKCB5nQcrJcDeKVNnO/GeWQ5gZfjpK+66iqpQnL/ySefNKecckp24JVTBGhgCmBw6Q5icO3+++8fCPDSf3I5novRo0dnBd758+fbo8/d+5u6vZMnTzYcV1XHPfPMM4aXBIcphJz0eXwJk48wfYeTPVzXBbychCmFxHcztw0LTfHRPn3glTTx2/KkPLT4Abxjx47tAG9MHsLHry8ay5VXXtkVLXzF70pseYHGK8Cbgn6oegyuucdGCV/xQ2WqxkFD6IjP5yka7x577NFDRvL0JLSMQOOdNGmS4Qh04SF+S9Kd/gkdlyZ9h0NExblpbljSm/rQ4ofGK8Abk77UK0RTgFfS8OUn5WL5wgPgpc/WcZRFU95hhx3MT3/6U3sW3hNPPFGJBMDL1z1O6mCBlwuOd/fPfq9EtUWmEPC2INe3KMDLpxRvr1xu9uzZA9F4c50yjBz5bHM13tSyHaTG+9xzz6VuXoc+wEv/yeVWrlzZAd5cPAV4c/GDTxONV+qHcvryl7/cvvj//u//3hxwwAFm3rx55vHHH5cs1heA5aJU42V6BYiOo1CO34QJE8yjjz7a4ZWa94oVKwzmDdFaUreR9sydO9dcd911yeTqy8x9eFK3D/o4zFQXXXRR5z6m5Au/RYsW2Y6/1157Wf4p+UkbH3744c4YSGx+NMKlaRtljLn88svNnDlz5NLm8fO65ZqEfXp8EcrLpQm9OmXgzUsUEyfl3Lq44To0++WFrnu8e7/8brqtoDFmxowZZoMNNrB9cM011+wCYb5ufU0YG2+hqQHgPfroo+3ABYMXCAQ/1s+lJ+Hf/e53dvAgxEPyhNLqxLl00CB+85vfGN6ydWhUyQsfl5eU4bOfzixp4kt6TB/aV199tTnwwAPtp1BKXlJveLASaNiwYZ02umkSbutLW/D5MsPU8LnPfa7nPpIuedvypLzQ45P/j3/8o7XzSVwM+i4Plx486DsjRozoak/Mtrn8CPNc8Hz86U9/6uLp52tyXSQzPsEPP/zwrvuYqo1SB3COL7QqfPw8XPPiP+SQQ8xaa61l+yF90f29853vNL/4xS+sHFGEeGmjZIoDzDs2XkwNm2yySRcBl5iGu4U7lOUhb+GhXMeXat1Uti+d5yB2H5N7j7/22mt3TA4hPpIXEP72t79tZ1MJ8OJ3Ae+OO+5o+Hzbe++9k/yg/bWvfa1D+4Mf/KD58pe/3LlOxVfowuv973+/HZSRuNT+P/zDP5jPfOYzto2035WvK4tY9dhtt93M+973PrPrrrtmk+vOO+9sPvrRj2bjRz+ls2+11VbZeH7pS18yH/7wh+39c+9hrPsWovOpT33K0H9CaSniWJDC4NHuu++ejSdfLeBAivYU0aSv0meL0v14937zzH796183X/jCF8wrX/nKQkV1iy22MF/5ylesaRPTBJo9mq64DvC6Nl5JTO1PnDixcHpGCt6PPPJIZ3QxBf0QTex0fMLlcqy3P+200zozN3LwXbJkibXx5uAFj1tvvdV2eB6CXG758uV2UCYXP/hcccUVdoxAeLoPrsTF9seNG2dyzlXm0/3888+P3YxSelOnTrWTCUozlSTyjPGSEk1XtNuNNtrIAjK4ds8993QoMHPLNTWQ0AW8uefx5p7VwAKK3PN4sSvLPF55cMTv3JmIAZnHm3NWA3MisfNWdVXaX5aHh5VOn3PJMAMk2JZzgRLtp+/knMeLPXLUqFFZ5/EuWLCgM4+3av9pm6/JdDJ4ck8YONtll106oAvYcs00vDvuuKNLq5V69p3VkAp4ix4i3q7+PF6pbAp/EAso/OlkRbKI1V4B3twr16pOJytqv8T7fkguDO4AvKF5vKH8MeJyAa+0nzoPAnhlHm8MmVWhMYjpZGjYdRdQcF/46vn85z9vXvOa11hTBbJiRk8/NzDglYq5nYo4NF7WwOdyQwF4U7eVN/LIkSN75hWm5EsnZoqOf3+LePr5/OuichIvGi+2t1xOgJepiKmdyCMH8Aov2iRTEXPOcx8E8DJtti7wIhueqxNOOKELbEV+4of6hruAQtIHbmrg8z+XY/URpgaEmMv5Gm9qvoPQeF1TQ1EHLIoPyaMsL2mi8a7Kpgbkwl7OOU0Ng1oyzIpAcWX3XvK09dF46+7VwNzmIjOT1Fl8v36F08kowHQy/3OxiJBPuOq1Tw+B5zQ1MLiGkTv3Ruis8c7l3N3JfHmnqgPAy8htHcfA0b/8y7/YTX1Y9cN9YUbGhz70IfNP//RPdr6sS89ti2i8OYGXfnreeecVPnxuXWOF0XjdBRSx6BbRAVz4CmWTHFfeRfljxPMSxeaaix91ZjwCe2wMR73BFV6SAKw4aQ/tY7CNufyu69J4Zb29FHIzxg7DA5tyTo2XDS4A+9zAe+ONN8YWXyE9F3gLM0VOAHhnzpxZiSqfsQcffLD51re+ZV/2rOrDVsuEc+Lf+973WvstK4Muu+yyHpr0m0EALw8VmlKR1tNT0QYR/nOnR/80EGKFIiiYMTdCB8SZ1/vNb36zizv3j0UWTF8DfN37GwReKe1mlLi6vk/DvR4E8DIyzWYguRzCB3jddqfkPQjg7XcChbQd+/M3vvENu+oHWymzPbbddtvOrA/kQv2/853vWPBlfmfILCTAm3NwTffjTdNrc+3HK32QVsiZa25c29b94Ac/MOutt5659957LanFixcb5vJ+5CMfMYTR6sXBtxR4JWMqf1DAqxpv3DvaD3jhhswZDNtnn30scwYctt56azt9ya8NaXRaJqjzYLqOTivAm9PUoMDr3oV44VzA69ZYgNeNqxIuA2pMCmi3xxxzjN2EC8BlgQ+aNfvR+DPGBgq8fLoV7W9ZRRB188ALjTc38N5yyy11q9o4/1DUeGkM+xy89a1vtfMg+VxnddC73vWuzoYsfoNZZciUsZC5YRDAy1QiJt7ndLlNDbQNgEhpTvHlNwjgZTyClzvOB1O5Ft+vb9E1X3D/+I//aPs4CsY666xj902BDubUIQW8J554orW5IoiLL77Y2gnxYxm+fSENAngZHGElGRPT2bwGn0+PujfWb0vR9VADXtrJXMd1113XLp+k3mgBmBHYyalIDj/84Q8t8AI+vhPgzWlqYEYMG6MsXbrUr06y61zAi90dsw8bHbEUlq1T+WQuujcxG5wLeBkAY7ASfGEjINrIuIS/V3abtrFK9WUve5nVfBmIFTdw4JUbKb5oNVtuuaXhx+fl5ptvbo444gipc1Q/N/Dyecr6/te+9rUWaFh7/+Y3v9les3gkhRtqwEsbf/KTnxhW+DBAxb1n2lK/Lx1mNqDxslOW7wR4c5kaAN2ddtrJ1gdlIZfLAbwLFy60e3tsuummdkbJdtttZzbbbDP7HAIkqV0u4GW2Bv0JnGHgduONN7ZtZB+VOk6wK1SGATR4vOlNb+qaRz9Q4JUKi0/FP/7xj9sNOfiM46HkB1hxikIKlxt44cfORLKclrYzwARgrL/++kkWjww14EUG22yzjQWu0D11+4ObzmcbD0do1ktO4GU7SOrPS5P6nHTSSW41k4ZzAC8aPNuzygosNDX2GWBaHyCc+pisXMCLNv/GN77Rrj5D6WE2DXjTTwGQG0w/Leqr5GF65Ktf/WorN2y97t4MAwPeogqzi9Yvf/lLaVtyPzfw0iB2p0erEIcsMK2wi73s4SBpMfyhBrw333yz1QJ+9rOfVW4ei0De8pa3FIJ1TuDlxfmrX/3KAtOGG25oVjWN170p2HbliBraCYCk3vMjF/CCM7xMcNjq2dgplsN0+LrXvc7uJIfi+O53v9u85z3v6cyeYg74wG28Lgi/7W1vs0vwXAGQ7uZx09qGBwG8DA4BFK477LDDrM3zvvvuc6OjhIca8PKS4fML8KrqsLux45PMK/fL5Vy5hjxx3CtMRqsq8MozJ6vIeOG8TpDdUAAAIABJREFU/vWvT75hTi7g/e53v2u++MUv2nvJaSksAQ85kUMoLRTHniiMVzBDR8CccRz6LzZlnK/xwmNgsxqoMDeWnX14KDlA7rjjjuss5asrgJBQ/LhBAC+Da9wAPunYzpAHl2kmxx9/vF+9KNdDDXgxswC83/ve9wrb59/rr371q+aTn/xkR2PwC+YEXuHNQ7UqAy+aGprbUUcdZRey0Ef9lawiC3z/nrlpdcKpgVfqCc6ghR566KH2S2r//fc311xzTZ2q9uTlywwwZ/EEpgZxDORhJ6cPsxpwSGi8UjlGUhlB/djHPmbnd/KwYZRm5x9/eZ2UaevnAF650VJXBoewVzK4xMg+IPTrX/+6EFSkXFN/qAEvy6V5+7NQQrTHUNtEbtOmTbOfba55xs+f09QgvFlSD/CySUoul8PGS1uQPZt7M+gEiNBPUQzknqRsb2rglbofe+yx5hOf+ISRlzr9kSlfP/rRjxo/i8yKAND989TgyZFNbISOtostObupgQMmOZlTfmwaIyvHiGNysTi0YJaSMnE+5pI+oZ8KeFldxWextJFVKrItI4ddkoYxHxDmhrz97W+3b13ejLHdUANe2shnGNNs3Ck2oXbzEG6//fZ23XsoXeIGBbwMiK6qpgamcF577bXmoIMOMr/97W/NG97wBrvKMLRyUO5DDGDOBbxSZ3wAky8YNsxCEerXL92yTcK+qQEayU0NbHTMZwtmBQzQTN9ARcfxFqBSOG4iP9b9v+pVr7JCsQkR/1IBLwMQjADTWWknA0MySozWwgCT69gZCSBKYW4YasBLu5k3SQdndkDRvhVoumgPyKufGwTwYipalU0NInMWGOHYFY175u6OFgNohY/4gwBezF/MU2bRwzve8Q7DnPGUToDXlV9y4MXGgVbLj2lj7EQlFeAmC/BKw/mkY1oGb6PYLhXw0h7ah3YnvmgKAImADfn4sXIOLZD5rbHdUANe2suLSebBYko64IAD7Mgytu/x48fbzUV+/OMfdwYn+slkEMArNt5VbTqZyJr7xLPK/WAKGVM6MTmkmm8ufFMDL+3yHV+g4AxpH/jAB8y+++7rZ4l6zT7g2U0NfgtcQfBJ7k9XAXCxM6VYZpsSeKWdbvsIMwmd46Bdx94GaLxsrBzbDTXglfbxlcPADVMImcTOVxD2faaZYYbB+bKTsr6fE3ilTgK8YmqQeL9uMa9z2Hhph9sWAQhMgtjmXY1X2ubml7imfmrgpV7+EmhmNWB3ZTARO29IyYvZRtF4XRkl13hdZm5j6FTMq2P6CqOLsj8roIv2k2Kn/xTA67bJDdNubEmf/exnrUkB+xk/NAr2LGCfAr4AYruhCrzSTrQpvgrQqNwHwpWdG5Zyrp8TeIUvwIu2nsI8JDx8PwfwHn300fblx1Laq6++2pqFmF3EqDxmQfbmTelyAC8rD9nxjjnKzJ1nZSx7QfMcsojLV/7atDfUdwcKvFIh8ZlaxURjtB+WCbNcGDCiY8vgWxsBhMqmAF7hI+2Sa3wAguPkWY5J+/gxsLbffvv1mFjccm3CQx14aRvAy0tJBiBD7Q3JU/INAnhZzcW8c1lgIHVJ6ecAXj67WdbOc0g/ZQCRdjLtivtTdh9itD0H8PKSZ1c8Vq7xQqGNLN3/+c9/bhj8D7mY7R5S08loLLuTMfDEDAY6durliSmBN3TziEOTx5aJxoRdSQYWi/K3jR/qwHvDDTeYd77znXbghi+AJm4QwMvDg70T+eZyOYBX2sI8XgZ9WVpbBEaSFx9gigFOOYBX6o1myyApJr6y6Yox2iU88UXjdWWW1dTgVoYw9iRsLUUutgAGAbw8PHSukIvdPngMVeBlQJFd2jbZZBO7PwdfOWLb9WVTJBeJHwTwAkwckpjCBOa3X65zAq/wxPSX87BLFK+yhRpSr5g+M2hQhHK5vhqv7DcqHTx1xZj3SocWl4qv0GVGBTMpXNui8E7ls2SYlVa5HA8NC1Boay6HpoTpoMyh6XM0NrtE8XXDZy1TDX0n98qPd69l/wc5ZbhKGbd8kzD2eIA3p2PVo7siSninaq/s1ZDarivtwEfzlE2k3HjCKdoJTcwrOYEXjJNBS2ljR+PlMxhQQgMlY44f9jJG/HPwggdzaxncwtjOWyg2X1d2hPnxMmNmg+zABk83X+w6MD+RTynaGpt2iB7tYnAUrcVPl3aKLOjsfHWg6bLTF/s4UN4vJ9eUY029++PeyRxTVgQyVYdNrd08Ke4tM1HYcYrPxhT0abPIScLTp083MgIvMknl0yZkyD61vBhT8JH+IO3jmhcLuJOCn0tTeNPf4MeKSolz86UIM0MLnq7rAC+2D0YzmeLFSo6YPzRbnx72XfgBvsJT8onvl2lyLbTgwWfU8OHD7Qoz4dmEZr8ywpM2slJt9OjRPW3sR6NJOm3izcq0LfYGhX8TOnXKwJPpOEyzgp/wFBm4tNAY0W4YQGWA4/DDD7fah5vHDUOL9tBp+REm7sgjj7Q2YmbFcC3pkkdohOogaXV8eLAslP5Kudh9x68n1/A4+eSTbf+BP3wln/h12lCUV2jBjzBLa5Gj8Cwq1yZeeMIDoKc/xJZpUf3gybJv7PU5eMKDrzx3m0gAuAO8DHDxUKCK88kR64dNTGi5YeK4wWgwRekSH8NncjiDBoAvg3hcx6Dr0nDbRxhZMrDG2zW2XF2+bhgTA52ZmQMp2ujyIkw7eaNjauA65Hy5YJrA1MASatIkXXyhK9duO5AjA3SsquIEitRylTqg6fIwM+NGZCBpct3G92nRLmy8LDl30wi71214umWRMYt++CJkz2hX5m6+NmG33oRpI2Y4vpbg56a34eOXdenCE34skXbj/TIxr8G4QlMDwIvtI5Wjwb6jMnziiAvlkbS2PrQZ1QR4ucm5HMArK9dy8MQ+xyBW2VSt2PXgM5x5oDgGEtFouLf8ZLm0e28xgwC88+fPt2XcNDdcVE94CPAW5Ykdz2cp2lKV+sXinXtwjecCzT6njTfnrAa5LyiYKfaCEfq+D8YVAi8PQ0rg9SvDNZVBk3Bdyo6NFgjPVPOE3XZImIcnJ/AOYlYDc7JlcI19GZgTKntzcO07tA2At2hWg5/fvx7UrAY+G9GSYjvp8+ILffpOaHCNdD+vlGnjM/ME01/OKXM5gNeXVW7gZRwCZcR1XaYGgNevpJs5djgEvLF5uPQGNZ1sVQde93h3PlN5wSFrfNG8pV/hv1SBF42XT1Bx0ia5buv79HJrvC7w+nVp27ai8gAvQJjaue0B55hMkMvJPF6XXw/wuompwwq88SU8CI3XBd4qLWKNvGtqqFLGzTMojdcHXrdOKcKDBN4U7QnRzKHx+nxza7wKvH/+sx3Q482ey60OpoYmwMum2y+llWtMM1Lgjf/UKPAmHlwL3TLVeENSaRf3UtB4mWvMaQBlyzbLpKAab5l0mqe5pobmVOqVVOBV4K3XYyrmVo23V1AMUDHtzbWX9uYqjlHgLZZNmxQF3jbSKy6rpgY1NRT3jhYpdU0NLVjZogq8bSUYLq/AG5ZL21gFXgXetn0oWL4u8DLC7I4yB4mWRCrwlginRZICbwvhlRRV4FXgLekezZPqAm9zTn8tqcDbVoLh8gq8Ybm0jVXgVeBt24eC5fsBbxvtNsRQgTcklfZxCrztZRiioMCrwBvqF63j+gFvawYeAQVeTyCRLhV4IwnSI6PAq8DrdYk4lwq8ceToU9EFFL5E4lzrAorAXg1xRBumokuGw3JpG6vA21aC4fIKvGG5tI1V4FXgbduHesq/FBZQ9FS6ZoSaGmoKrGJ2NTVUFFTNbGpqUFNDzS5TLbtqvNXkVDeXarx1JVYtv2q8qvFW6yk1cqnGW0NYNbLqXg01hFUjqy4Z1iXDNbpL9ay6ZLi6rKrmVFNDVUnVy6emhnryqppbTQ1qaqjaV2rlU1NDLXFVzqymhsqiqpVRTQ19TA2xJ94PYlYDx7sXbYQeu330Po5t4cw1jjnK5YqAN0X7aNMgNF6Ob8m9LSTHRnFCdS63Omm8nLiTy5VqvDmP/pEHsmxbSMkTUzgCvDnPXENr4XBG38Vqn0/nqaeeGhLAS738uvkyaHo9CODlzDUOu2RHtVTtQh5CG79I45U8TeVXVG4oAW/MNvq0hpzGS4VyujLgjVkPEbwALx0sl+Ph4STVXE4Ou8yp8d52222dM9dSt5N7WQS8cp9T1IHBNc5ca7qVZZM6FQFvE1pVygwl4K1S36Z5Bg289NPO0T9ovFOnTu28cZs2KlROHgh8CZOPA+BQw3F+mpsvRLNqnEsX4AXsReONxUPqEqLHw+ObGiSf+FK+qQ8doSUaL23N5dzDLuHp1qdOHaQNbplQHMC75pprmj333NPN2hVuWocuIo4G6s9qiE1f+Lp0BXhFBr4vZdr4QhMacsowM2NwblobHlI2RM+d1SDpvi/lm/rQE5rQAHiHhKmBSnH4W06NF55nn322BV5XKE2FW6WcHO++qp4yjBzFxiuHTFaRS9s8aLxyvHtbWmXlpZ+ENF7SJF38Mlp101zgTUGf+vh0BXjr1rVpfp6LVfGUYV8eF1xwwdA67BKNV5zfCSS+iV9Eyzc1SD7xm/AqK5PS1ECdQ/UOabxSx1B+SWvqyzze3BrvrFmzOlUWWVRpn+SRMh0iJYEQ8Ep2oce1G5b0ur7QcIG3Lo2y/NJu4SPXlHGB142XvGV0m6SlNDW49Xfr5mq8El+UV9Lr+EJLfMpyyvBdd91Vh0yrvO7gGvXAdUwNVMQF3lacKhbG1MCgRS7H0eOAPUfP5HJz5syxNslc/J599lkzZswYQ1tzOU4NnjlzZi529qy2NdZYw+y1116Wp3TmlBVYsWKFmTJlSkoWPbTpO/PmzYvyAukhHojguTjrrLPMypUrA6lpojh3L+eXNq0AeO+55540DQpQBePAHXH01w7wYmo45ZRTDDebN23qH9OsTj75ZCsEwin5Cf2LLrrInHjiiWb27NlG4lLyhTYgOHHixI5cmSIUk6dLjzaheQ4fPtzMmDGjwzMmP58W/YUX6GmnnZZEprSJNsqP6VUjR440AC8HZl5xxRWdNOom8hDfr2+Ta+owbdo0M2LECEs/Vd8RuvjIlb4zbty4LPcRnjwXJ5xwgu1DUpcm8qpTZtKkSVauufjBh/7DQGkOrIMfLxYwwHUWeEHgpUuXWuClY8f+zZ07N0iTjgwYhvgVlQnlLYvjwZR0tDJ4InCJS+3z8GDLdvm4dXLjY4QBnOOOO84+PDHoVaHBNCvmDlfJWzcPYMDLhB/3j/ZxDwV4uSZe8uCnuL+8yEQxqduGpvnHjh1rzjjjjC65puw7yA3FBJk2rXPdcry0Tz311Gz8qB/8sPPWrWvT/Ly0e4BXPtMwNUyfPt0F5ShhoR8ixgO7fPnyUFKSOD6/4ZnT0ZlvvvnmZCx9+TJAAtgzu8FPS1UJTA2XXHKJJZ+D56JFiyzwiqlB2pWS9yOPPGIfVuGVw6fvXHnllV2s3Da64a5MNS58Gpga6EN+fA2StbJyL93ZVLH5uvQkDL977723Vj3bZAbjUL5c1zE1ALzYPnI6f3AtNW+ZTpZ7Hm9oAUWqtjKrAeDNOY/Xn06Wqm1Ct2xwTfLE9lMNrpXVk092tKxcjulkzGqgD+VyKCW5bbzwGxLTyRAywOsLQN4QqW4CnxkPPvhgh3xqfgK8OaeTYePx5/F2GpwgIPN4cwEv96xoyXCC5llNzAVe6TP48kvBF+CVlWsp6Ido5gBekR/8UUjGjx9vZB5vqE6x4wBePvtDzq1bKL1pXE7gpQ3urAap88A1XtbAuy6VsKEr08lkAYXLN1WYhycX8NLGQczjBXiZx5vi3oVousCb6r75dAFeBmRy953cGi+mhpzAG5pO5ss+9jVAj6KZyw0UeEMPkK/xphaEAG9OU0NujZeHhhkGuTRe7lnuJcMswWZwzV25FupfMfsTU4LYJCfnVMQcGq8ro5TzeF0+blg0Xrl/4rt5YofReIcE8NJYsfGmaniILgZnX+NFyKG8TYXv0lpdgDe3jdc1NSBvV+ZN71tZObQkH3jL8sdI8228qdsI/dUBeF2NN7VMpR8MEniljQM3NcheDSKUlL4Ar9h4RQgpeeY0NdAOWbmWU+N1gTe2LEP3yDc1hPLErocPvLHph+gJ8KZun9BH4x2UqUHqEJJD7LhBAC9f924bV0vgzWlqUOCN/dgMZj/eQQJvfAmGKQ7C1OBqvOFaxY8dBPC6K9dokQJv/PvaRVGBt0scUS58jTcK0T5EFHj7CKhhsgLvajKPF7uyarwNn5KCYilNDSGWCrwhqbSPU423vQxDFAY6qyFUoUEsoFDgDd2JdnEKvO3kV1RabLxF6bHjFXhjS/Sv9BR49bDLJD1LgTeJWFe7WQ1ppNhLVW28fQ677BVZuxiZ1aCmhnZy9Esr8PoSiXOtGm8cOfpUFHgVeP0+0fp6VZtOFhKI2nhDUmkfp6aG9jIMUVBTg5oaQv2idZxqvK1FGCSgGm9QLK0jVeNVjbd1J/IJqMbrSyTOtU4niyNHn4pOJ9PpZH6fiHKt83ijiLGLiJoausQR7UJNDdFE2UVITQ1qaujqELEu6pga3GWTTfkr8DaVXHk5Bd5y+TRNVeBV4G3ad0rLVQVeAV3xS4mWJCrwlginRZICbwvhlRRV4FXgLekezZOqAi8c2oIuNBR4m9+rspIKvGXSaZ6mwKvA27z3lJSsCrwxQJdqKPCW3IwWSQq8LYRXUlSBV4G3pHs0T6oKvM05dJdU4O2WR6wrBd5Ykuymo8CrwNvdIyJdVQXeJ5980nA8+bhx48ykSZOs5tqkCgq8TaTWv4wCb38ZNckxZIFXPkHFb9K4KmVWpyXDtDWXqwK8HBT59re/3Wy++ebm3e9+t3nb295m1l13XbPvvvvao+ilrlX6wKCBt0odpT1t/NVlAcWUKVPaiKl22SG3gIIKpXKhzjrI3clC9UnR9tzzeDnsMveZaxzvPmvWrFLxjRw50vzhD3+wp0o/++yz9qQM7v/aa69tTjnlFFu26j0ZBPDKmWvPP/98aTtjJpYBb1VZ1anPqqzxuvK68MILh8aZa9wcOXOtzo1qm7cMeF1BteUj5TkOh20hc58Um+uUYdoppwwPlaN/5D6KL/dCfLTfXXfdVS4r+ax24sy1PfbYI8osiSpMhxrwVqlz3TwCvPShXK5s5VpRn2lbNxTMu+++uy2ZyuVLTQ133nmnPd8e4cuPs8kkHNMH+KCNnW/ZsmUdHqn4Sd2XL19ueT7zzDOWv8Sn9C+99FIzf/78ThtT8kJ+jz32mDn99NPNihUrsvCkPYsWLTIzZswI8uNek8f15aRe7sfrXvc689Of/tSmU3/JRxmuV65cadCQ+RHmhzwB3t12262TLmnkk34kfgyZP/jgg4Zzs+AjdYtBt4zW7NmzzZw5cwr5ubJqWhdXRgDu+PHjbR8qq1dTXqFyKCWTJ0/u9B23PqH8MeIwbSxevLirr8WgW0QDjEPJdF3n6J+lS5eaY445xpx55plJfxymBw/8Y4891oJELp5jx461POlcqXkK/RNOOMF+Sku7JR4/FOemNwkzcHXkkUca2pqCfqhOmBGOP/74Upkic36jRo0y5D/iiCPMJz7xCQu8Rx99tH0huvWV8OjRo638KINJguuDDz7YAu/222/foUfaqaeeakaMGGEH70L1bBPHy2zYsGG2DbH7j7TVrx9958QTT+ySq5vXDftlm1yfccYZ9vmgDzUp36QM93X48OHBvhqjfT4NruFHP2xS3yZl6JcTJkxwcbf7zDXePGyywpvvqaeesmGuU/0mTpxolixZkoUXbUBrQQBohana5NO9+OKLzbXXXpuUn3uv0HQBp4ceeigpT7ed2FynT59u+aGxoInxwx6KFkB/Ij9axg477GA222wzC5zbbbedue6662wel56EKRf6IU803t13391qwuThK8bNKzRi+ffcc4/VWpiZAZ9YdEN05H5iN+eLiTwSF8ofK+6JJ56wLy36UCya/ejw9cLAa798bdNd+Z1//vmGcYm2NKuWR6nl6951HY03l43XtduU2XjdSsYIwxfAzW3j5cHhc8ptd4z2FNEAFNDOaGsud9ttt5mZM2dadoDrvHnzzFVXXWV9zBDi6KiAyQUXXGC1xy9/+cvmrW99q5k7d65kqeT3G1xLIWvZnUzMJJUq2iCTW3cG15h+l8vxskSjow/lcjfffLPtD6n4IU9XpvDJbeNFCRJTg9SlB3glIaUghHZO4IXnoKeTpZCtT5M3O8Cbe3BNZjUccsghZoMNNjAbbbSR2XDDDQ3XRQ5tGPBlmhn1rupc4PXbX5VG1XxCX4B3qMxqqFr/Ovm4H5hReEHmcmWDa6nqMOSmkzHNIqdb3YA3h2x5aAYBvKLxAvgPPPBA59dvPjF20/XXX9/wOSYg109OLvD2yxsrfXUBXjReBd5YveavdEpnNeQyNbhNUuB1pREnPGjglVa4IOqG/fRvfetbZquttjLYF6s6Bd6qkqqXD41XgbeezKrkVuDVJcNV+kmtPIBqv5VraL0HHXSQta+j2T766KMGu/Chhx5qXvGKV9hZGHWYKvDWkVb1vAq81WVVJ6cCrwJvnf5SKW8V4GXGwfe//31r9910003NFltsYfC33XZbu8qOQZ06ToG3jrSq51XgrS6rOjkVeBV46/SXynnReGVwzS3kmxhE0yU/K4dY7BByfjk/jwKvL5E41wq8ceToU1HgVeD1+0SU65CpoR94tmGswNtGesVlFXiLZdMmRYFXgbdN/yks6wNvStClEgq8hbeiVYICbyvxFRZW4FXgLewcbRIEeFMDrtRRgVckEddX4I0rT6GmwKvAK30hqi/AG5VoCTEF3hLhtEhS4G0hvJKiCrwKvCXdo3mSAm9z2ZWVLNuPt6xc0zQF3qaSKy+nwKvAW95DGqYq8DYUXJ9iCrx9BNQwWZcMn3OO4W2Qyw16r4Yc7RwqK9dStlVNDWmkqxpvGrmqxqsab5KepRpvErEa1XjTyFU1XtV4o/cs1Xiji9QS1E1y0shVdye76y6ju5PF71xoLTnPXFPgjX8PoajAm0auCrwKvEl6lgJvfLGqjTe+TKGoNt40clUbr9p4k/QstfEmEevAbLw5T6BYHTRejhyTEyjoKSw06jmBIk0XClP19+NNvfJpdTrePefRPzmA1+0bPKycubbnnnuGO1aC2NXB1DCIo39WB+BVjffPf7aHzvFJlcsNytTQ7+SHmO3n4EA5gSIm3SJaamookky7eDU1tJNfUenVHnjReDntc1UEXtEIZXAtt8Yb2hayqCO2jReNd6+99mpLqnL5VVXjlX6DINB4OXNNTQ2Vu0WljKs98LIfLKcMcwR5Lpdb4x3UYZc5Nd6bbropu6nh4YcfNhwLviofdslzoUf/xEcGF3jlRTekbLzxm9xNcVXWeKWlovHS1lwOG+/FF1+clJ10WHzReNXGG1fkfAmqxhtXplAbksDLmfO5nGi8q6KpQWQ4KODNaWrAxrvmmmvq4Jrc9Eg+Gu9ZZ52V9ZThm2++2VxwwQWRWtCfDC9uVq5xAkouB8a5sxrgO3CNl084HAIRrSaVQB5//HErgBdeeCEVix66c+bMsRt39yREjhDZrVy50owZM8Y8+eSTkTkUk1u8eLGZPXt2cYbIKbfccos1Ney9996RKReTW758uZk8eXJxhgQpmKkuv/zyBJR7SdJ/eC4AXvpQLrdw4UILhLn4wYeFYhy6msuBcZg4XdcB3iVLltgHls84NAp+bljiYvnQPu2008wVV1yRlI/UF35XX321GTVqlLnhhhsMdsLU7aNTMZg3derUZLykDfj85s+fb0488URzzTXXJOMpMsWHJ2YGHlipi5veNrxgwQLbJtp13XXXmeuvv97yYjrZZz7zGXsvSXN/3Nu2fN3ytGvevHm2v8am7fJxw/Ck76ApoRW6aSnC8OO5OOWUU6wsU9zLUL2nT59ucSeUFqMOPg1kOXbsWKsohHjGjoP/3Llz7b0sBF6Ejobm/i677DLT5gctyosvtLg++eSTLSiF0vw4KdfEhxa/GTNmWJ6XXnppT32a0KWM1FN4CB2uETja58SJEzv5/DKSv6kv/IUun/zDhw+3YOimNaXfrxxtPO+88ywoSR1cv195SfflJ/EXXXSR1VB4eaGpcA+PO+44q/F+9KMfte0kTdLJg/ZNvYRGW5+6TZs2zYwYMcIuahC5it+WvpQXGeBL3xk3bpwNCy83j8RJ+Sa+Sw+5nXDCCfbg0hi0y+ojfNEER44c2fV8lJWrm+a3A7mCc5g3/LS6tKvkhwd9EgxwXUfjveuuu2zndRPl87+NL/TkU1hoEc8Dyycczo13ryW+rQ9NTA3caNfUEIOuW1/CruPmoCXh4OW7tvyFpvic3AvYP/HEEx2eMXgU0YAJpgax8Uo+4iXcz3fz2kr3+UOLqLqAoh/vfulSlUceecRMmTJFLq3fr2yVdAiF8hFP30HTljy+HypXN84S/9sfz8WECRO6TA116fXLL/zIh+Or0LXxSnnSJBzDF774vKTFxhuDdhkN+GFqOPfcc7ue/y7gBZkhkssBgoz45XIsKuDTLffgGp8vueTK4BrAm2tWA+1iVoMAb457yYvMB17p/Kn4M0CCjTfXdDLaI8Cbq+/wXDCdjCmJORzt4tlgsCtXG+Ejg2u5eIJxhTZeNF6AF0eF+PEGlHAMH9pCk7C/ZFg00Ri8fBrwA3jdBRR+ntjX8GSABNsZLjZ9nx48/FkNfp7Y1/B0lwzHpG+FFvjjYQV499hjj0DqX+VMQqy6QAvgZR5vij4aqitx9B0+jYvSY7UPOjiZxysLKGLSD9GCJzZX+ZKQeoTyxoqDJ8B755132jbHoltEByb+Xg3EdWm8VCin84E3Ne9BabxiakjdPuijrTBomVPjve2cvSnwAAANJ0lEQVS225JpvHRocRIOabzkkXTJH9MX4M2p8QK8DD7ncjKPN5fGS7swG7mmhtRtpY8MQuMF63DSRzvAi81DNF5pvGSS66a+T0eui4BX0pvy88tBjx/Ai8ovpoYUfHzersbrp8W8lrb4Gm9MHkW0ivZqkDoVlWsaLzbekMYLT+ErflM+brmUwCv19H36jjudzE2XsFvHpmGhJaYG0Xib0qtSTni6wCtxUt6/lvi2PsDLF34u5y6ggCft6gCva2rIVSEMzmU23tiC94E3Rzt5eNgIPXZbiuo+COB1TQ1F9YoZj6lhdV5AEbsvCT2AN/cCijLgjdlnXFqDBl7qMlDgLdJ4XSHFDA8SeGO2o4zW6gK8/uBamUxipK2qm+S4shGNlz6Uy7nAm4unAq+euRa9rynwRhepJajAm0auCrzOrIY0Iu6lqhpvr0zaxijwtpVguLwCb1gubWMVeBV42/ahYHmx8QYTE0Qq8CYQqh52mUaoA5jVQEPU1KCmhugdWoE3ukgtQdV408hVNV7VeJP0LNV444tVFlDofrxxZauDa3HlKdT86WTE66wGkU4iX4E3vmAVeOPLFIoKvGnkqsDrLaBII+Zuqgq83fKIcaXAG0OKvTQUeHtlEiNGgVeBN0Y/6qExiAUUOo+35za0jlDgbS3CIAEFXgXeYMdoG6nA21aC4fJ8LblLhsO54sUq8MaTpUtJgVeB1+0P0cIKvNFE2UVIgbdLHNEudDqZTieL1pmEkE4nE0nE9XU6WVx5CjWdTqbTyaQvRPV1cC2qOC0xHVyLL1MoqqkhjVzV1KCmhiQ9S00NScRqN0JXG2982aqpQU0N0XuVmhqii9QSVFNDGrmqqUFNDUl6lpoa4otVTQ3xZQpFNTWkkeuQNDVwHlEuN1T245WNp1O0WzRe2prLVTE1cFYZWuOyZcu6fg888IA966tOXVdV4HX7BeGiWQ1uvjpy65d3dQFejhri4IdUcvTlXAq8cvRPrspQObaFXB2B178xMa8FeHOduUbdqwAvL4IPf/jDZtNNNzVbbLGF/W2++eZmq622sudu1ZGBD7w5+mzKo3+K2s4pw76NN2VbBXhzHP0jbeZe5jxzDb4ccSaHXUo9UvqlwEtFOG8+p8u9H++jjz7adeZajrauDqaGKoddotlutNFG5rDDDjNz5swxl156qdXoCD/++OOdWyHAIn4nwQn4wOsk2WBZWT9v1euHH37YnjKc67BL6iUab4r2hNoN8HL0z6p82CXtHtKDazludm7gRQt0D7sMdb7YcasD8BYddunK8o477rDAO3/+fDfahuv2taJThnsIR4yQwbXnnnsuItVyUiGNV0rUlZmUK/MB3vHjxxu+mnK5QQ2u5dR4+VrifEnXde1ONm3aNDctWVg6zXnnnWeWL1+exdYCTzQrwD6nQ6Ojc+VyPDxjxowxTz75ZC6WBlCdPXt2Kb+FCxea9dZbz+Ytyij9QvyifIsWLTLs1bD33nsHs/QrHyxUEgm9Rx55xEyZMqUkV/wkgHfevHnxCZdQnDBhQucU7pJs0ZJuueWWntPNIR77HroVxtRwzz33uFFJw2AcCp/rOsC7dOlSc9xxx1k1HFU89g87DjRd//jjjzeTJk3qxMXmKfSEJ6ALTx4gSUvtjxw50owdOzZZG6Vt4p9//vnm2GOPtS+Y1G0T+meccYYZMWJEUKZ08unTp1sTwyte8Qrzu9/9zhx55JHmmGOOsdrVxRdfbHjhCy1ph1xzryZPnmw/8/GJP/roo+0pw9iMuabN/EjnJzTEF1pNfKFBPz3hhBM6tJvQKiojPMSXfKeeeqrhxzVp8pP0mL7QHjZsmJVlTNpltHg2TjzxxML7X1a2bprIl/t45plndnjWpVM3Py8zfq7rAC+Da1SG0b7YP2iHaKKZLViwoJNWlC9Utkkcn6jwXLx4cYdnEzp1ygAIs2bNCvKL0V5ouHTQBgFBtOw69WyTd+7cuRboocELHG1CflwvWbLETJw40ZoaGFDbcsstzYYbbmjWWmst88UvftFgsxX+blsI33777XbwDjsyP655gNB4d955ZxsnaeKjgbt0hHYb//rrrzfjxo2zGju0Y9Onbi5dwvQd2ippbv1j8hdaPBejRo0y9CGXV8owX0rgjtTB91Pwht9VV12VrY2Y13hxu1p8B3hpoAyuuRlclI4dxtTAoIXvUvEXU0Mq+n47uAaUAJZc7tlnn7UvlyeeeCIXSwuGl1xyieWHHZ2ZKozkMqD22GOPdeoBIBLHIOd9991nRo8ebdCCf/nLX3byVAnweQrw7rXXXlWyR8mzYsUKq01HIVaRCGaqHKYG93lgcG3lypUVa9g+GyYoNMicjq8wFIJcDozzTZxdwEuFcrrcg2tDZR5vShnnnk7GQ+tOJwNE0WaZNsYshoMOOqi0ufvvv7/Nix2squs3q6EqnTr5ZHBtELMa6tSzTV6ZTrY6DK6haOZypdPJqIgCb/xbsTrManCBl8/UmTNnGjRgfNJcjcqXMPbh9ddfv5YGosDrSzHOtQJvHDn6VBR4dZMcv09EuXaBtypBAeP99tvPbL311l1zefvRUODtJ6Fm6Qq8zeTWr5QCrwJvvz7SKL0IeAVcIcp0GgYZsAHzgGP2wZ64zjrrmKOOOsrydfOXVUSBt0w6zdMUeJvLrqykAq8Cb1n/aJzmA28IQNFsN9hgA7PNNtuY9773vXap8CabbGJ+85vfGAYE6zgF3jrSqp5Xgbe6rOrkVOBV4K3TXyrn9YE3VJCH+sYbb7TTo5gmxQwappk1cQq8TaTWv4wCb38ZNcmhwKvA26Tf9C0TAt6Q1tuXUMUMCrwVBVUzmwJvTYFVzK7Aq8BbsavUyybAmxJs3Rop8LrSiBdW4I0nS5eSAq8Cr9sfooUFeKMR7ENIgbePgBomK/A2FFyfYgq8Crx9ukizZAXeZnLrV0q2heyXL1a6Am8sSXbTUeBV4O3uEZGuFHgjCdIjo8DrCSTSJUuUdeXaf/1XJHH2J6NLhvvLqEkOBd4mUutfRoG3v4ya5FDg1VOGm/Sb0jK592qgMgq8pbekcaICb2PRlRZU4FXgLe0gTRIVeJtIrX8Z3SSnv4ya5BjUCRRqalBTQ5P+WlhGgbdQNK0SFHhbia+wsAKv7k5W2DnaJPC5yIqtXE6BN42kFXjTyFWBV4E3Sc9S4I0vVp3HG1+mUNTpZGnkqtPJdDpZkp6lg2tJxNo53j0N9V6qCry9MokRo8CrwBujH/XQUODtEUmUCJ3VEEWMPUR0VoPOaujpFG0j1MbbVoLh8mrjDculbazaeNXG27YPBcurjTcollaRauNtJb7CwmpqKBRNqwQ1NaipoVUHKiqspoYiybSLV1NDO/kVlVZTg5oaivpG43g1NTQWXWlBNTWUiqdxopoa1NTQuPOUFVRTQ5l0mqWpqaGZ3PqVUlNDPwk1S+9rapg2bVozyn1KFW2Qfe655xo0iVzuscceM/B84YUXcrE0l112mQEocjnOLxszZkytU3vb1I17e/vtt5tZs2a1IVOr7MKFC80aa6xh9tprr1rl2mRevny5mTx5chsStcvSd+bNm9cpV/QcdTK0DPBccADpypUrW1KqXpx7yae/61K388ILL2x87JRbz6phMO6cc87pyr6GXLF2+cwzzzQPPfSQAaFj/Vx6Dz74oKUrcWPHjjUInmuJi8U3RAeAAJTuv//+rnqE8saKu+CCCyz4SvvwRQ6xeLh07r77bnPyySebxYsXR7uHLn0/THuuvvpq+0KTNvp52lwvW7bM3i/uGT+uZ8yYYYF3xx13tNf33Xef4Sd5Hnjggahtp12LFi0y48ePt/zatMcvWyQz4uk7KENFeXxaTa+FPvIbPXq0BaWmtOqWu/zyyy3YSx3qlu+X36fL9YQJE+yJ135aP1pN02+++WbLU7AWvwO8aIMcQsgx3KBzrB8aJrRCdHm7+vGSPxZ/lw68QjzdPLHD3GR+0i63vW44Bl/ouW0UnjFoF9GAx6RJk7raSN5YbRP5iT9x4kQLDj//+c/NYYcdZrjmnro/6lNU36bxIteYbQvVxZUbbaZ95MtxL6WNbh1CdYwZJ30nJs1+tJArfHPIlLrAb8GCBS7uvgi8XbEZL1J/VmRsSimrVbWdbrvccKkwGiSmpF2lOjn5+7z86yr1bZInF58mdUtRJkd7hYf40o6OxusnkCEUJwXr+kLL9106kubGtQ0LTd9vS9cvD33hEUqrEufnqXNdxr8OnRh5m9SlbpkiWceo/yBoSHvED9WhLC2Uv01cbF7Qi01zKLWvbl06wCsFBy2cQfMXOcT2cw7oxa77UKDXr1+Q3i9Pm3YIbfHb0KpS1uXjhquUbZonFx+3frl45uLjtk3CLm8J9wAvmSVRCrbxoSW/frSFr/ht+LplXf5ufOxwv3pLuu/HqofQFXr+tcQPVb9OfavkrZKnjixi03N5u7TdcCgP6UV53PxDLVy3znXzh9obg0aIbtu4/w8DUrVOVpcpIwAAAABJRU5ErkJggg==[/img][br]Translate [math]A[/math] by the directed line segment from [math]\left(0,0\right)[/math] to [math]\left(0,2\right)[/math].
Translate [math]A[/math] by the directed line segment from [math]\left(0,0\right)[/math] to [math]\left(-4,0\right)[/math].
Reflect [math]A[/math] across the [math]x[/math]-axis.
Rotate [math]A[/math] 180 degrees clockwise using the origin as a center.
[size=150]For each point [math]\left(x,y\right)[/math], find its image under the transformation [math]\left(x+12,y-2\right)[/math].[/size][br][br][math]A=\left(-10,5\right)[/math][br][math]B=\left(-4,9\right)[/math][br][math]C=\left(-2,6\right)[/math]
Next, sketch triangle [math]ABC[/math] and its image on the grid above. What transformation is [math]\left(x,y\right)\longrightarrow\left(x+12,y-2\right)[/math]?[br]
For each point (x,y) in the table, find (2x,2y).
Next, sketch the original figure (the [math]\left(x,y\right)[/math] column) and image (the [math]\left(2x,2y\right)[/math] column). What transformation is [math]\left(x,y\right)\longrightarrow\left(2x,2y\right)[/math]?[br]
Here are some transformation rules.
Apply each rule to quadrilateral [math]ABCD[/math] and graph the resulting image. Then describe the transformation.[br][list][*]Label this transformation [math]Q[/math]: [math]\left(x,y\right)\longrightarrow\left(2x,y\right)[/math][br][/*][*]Label this transformation [math]R[/math]: [math]\left(x,y\right)\longrightarrow\left(x,-y\right)[/math][br][/*][*]Label this transformation [math]S[/math]: [math]\left(x,y\right)\longrightarrow\left(y,-x\right)[/math][br][/*][/list]
[list][*][size=150]Plot the quadrilateral with vertices [math]\left(4,-2\right)[/math], [math]\left(8,4\right)[/math], [math]\left(8,-6\right)[/math], and [math]\left(-6,-6\right)[/math]. Label this quadrilateral [math]A[/math].[br][/size][/*][*][size=150]Plot the quadrilateral with vertices [math]\left(-2,4\right)[/math], [math]\left(4,8\right)[/math], [math]\left(-6,8\right)[/math], and [math]\left(-6,-6\right)[/math]. Label this quadrilateral [math]A'[/math].[/size][/*][/list][br]How are the coordinates of quadrilateral [math]A[/math] related to the coordinates of quadrilateral [math]A'[/math]?
What single transformation takes quadrilateral [math]A[/math] to quadrilateral [math]A'[/math]?[br]

IM Geo.6.2 Practice: Transformations as Functions

Match each coordinate rule to a description of its resulting transformation.
[size=150]Draw the image of triangle [math]ABC[/math] under the transformation [math]\left(x,y\right)\longrightarrow\left(x-4,y+1\right)[/math]. Label the result [math]T[/math].[br]Draw the image of triangle [math]ABC[/math] under the transformation [math]\left(x,y\right)\longrightarrow\left(-x,y\right)[/math]. Label the result [math]R[/math].[br][/size]
Here are some transformation rules. For each rule, describe whether the transformation is a rigid motion, a dilation, or neither.
[math]\left(x,y\right)\rightharpoondown\left(x-2,y-3\right)[/math]
[math]\left(x,y\right)\rightharpoondown\left(2x,3y\right)[/math]
[math]\left(x,y\right)\rightharpoondown\left(3x,3y\right)[/math]
[math]\left(x,y\right)\rightharpoondown\left(2-x,y\right)[/math]
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[/img][br][size=150][br]Reflect triangle [math]ABC[/math] over the line [math]x=0[/math]. Call this new triangle [math]A'B'C'[/math]. Then reflect triangle [math]A'B'C'[/math] over the line [math]y=0[/math]. Call the resulting triangle [math]A''B''C''[/math].[/size][br][br]Which single transformation takes [math]ABC[/math] to [math]A''B''C''[/math]?
[size=150]Reflect triangle [math]ABC[/math] over the line [math]y=2[/math].[br]Translate the image by the directed line segment from [math]\left(0,0\right)[/math] to [math]\left(3,2\right)[/math].[/size][br][br]What are the coordinates of the vertices in the final image?
[size=150]The density of water is 1 gram per cm³. An object floats in water if its density is less than water’s density, and it sinks if its density is greater than water’s. [/size][size=150]Will a cylindrical log with radius 0.4 meters, height 5 meters, and mass 1,950 kilograms sink or float? Explain your reasoning.[/size]
[size=150]These 3 congruent square pyramids can be assembled into a cube with side length 3 feet. What is the volume of each pyramid?[/size][br][img]data:image/png;base64,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[/img]
Reflect square ABCD across line CD.
What is the ratio of the length of segment [math]AA'[/math] to the length of segment [math]AD[/math]? Explain or show your reasoning.

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