IM Geo.6.3 Lesson: Types of Transformations

[size=150]Point [math]B[/math] was transformed using the coordinate rule [math]\left(x,y\right)\longrightarrow\left(3x,3y\right)[/math].[br][/size][br]Add these auxiliary points and lines to create 2 right triangles: Label the origin [math]P[/math]. Plot points [math]M=\left(2,0\right)[/math] and [math]N=\left(6,0\right)[/math]. Draw segments [math]PB'[/math], [math]MB[/math], and [math]NB'[/math].[br]
How do triangles [math]PMB[/math] and [math]PNB'[/math] compare? How do you know?[br]
What must be true about the ratio [math]PB:PB'[/math]?[br]
Match each image to its rule.
Then, for each rule, decide whether it takes the original figure to a congruent figure, a similar figure, or neither. Explain or show your reasoning.
[math](x,y)\rightarrow\left(\frac{x}{2},\frac{y}{2}\right)[/math]
[math](x,y) \rightarrow (y, \text-x)[br][/math]
[math](x,y) \rightarrow (\text-2x, y)[/math]
[math](x,y)\rightarrow(x-4,y-3)[/math]
Here is triangle A. Reflect triangle A across the line x=2.
Write a single rule that reflects triangle [math]A[/math] across the line [math]x=2[/math].[br]
Write a rule that will transform triangle [math]ABC[/math] to triangle [math]A'B'C'[/math].[br]
Are [math]ABC[/math] and [math]A'B'C'[/math] congruent? Similar? Neither? Explain how you know.[br]
Write a rule that will transform triangle [math]DEF[/math] to triangle [math]D'E'F'[/math].[br]
Are [math]DEF[/math] and [math]D'E'F'[/math] congruent? Similar? Neither? Explain how you know.[br]

IM Geo.6.3 Practice: Types of Transformations

Complete the table and determine the rule for this transformation.
Write a rule that describes this transformation.
[img]data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAANsAAAEYCAYAAADViIPuAAAgAElEQVR4Ae1dCcxVRxnFfQGsGwrFhdVWKA2yyCogULWCKVJA0SpFEGugoRaXKFsqlRIJoBBAUJQlUkmDpLFxY6k1wdhGQKAILVVDqbUFtNVqUbYxZ+K83He3M/e9u8zMm0lu73tzZ775vvOdM3PvvPuXNsIXj4BHoBQE2pQyih/EI+AREF5sngQegZIQ8GIrCWg/jEcgUWyvfdlLhD88Bp4D2TiQNqWkii2to7/mLgIQmC/ZEWC4ebFlx9T5How0zgPQYIAMNy+2BoF1uRsjjcuxNxMbw82LrRl0He3LSONo2E2HxXDzYmsaYvcMMNK4F3E+ETHcvNjywdkpK4w0TgWbYzAMNy+2HMF2xRQjjStx5h0Hw82LLW/EHbDHSONAiIWEwHDzYisEdruNMtLYHV1x3jPcvNiKw95ay4w01gZWsOMMNy+2ghNgo3lGGhtjKsNnhpsXWxlZsGwMRhrLwinNXYabF1tpqbBnIEYaeyIp11OGmxdbufmwYjRGGiuCqMBJhpsXWwVJMX1IRhrT/a/KP4abF1tVmTF4XEYag12v1DWGmxdbpekxc3BGGjO9rt4rhptRYnvmmWfEjh07xPPPP58JuUcffVTcf//94uLFi5n6scarV68Wd955p9i2bVti02effVbcfffd4pOf/KT4yEc+Iu644w7xpz/9KbG9DRcYaXRjKCovuuOX3Y7hZpTYbrzxRtGmTRvx2c9+VhunCxcuiKuuukr2++EPf6jdT6fhkCFDpN2Pfexjsc0PHTok2rVrJ9vAb3U88sgjse1tqWSk0YmjyLzojF9FG4abUWJbsmSJeM1rXiO+973vZcLqhhtuEG9605sEyJ9nYWIbNWqUFFjHjh3Fxo0bxcMPPyzWrVsnLl26lKcbpdtipNF1qKi86I5fdjuGm1FiAziYERspjfZLG4uJTa2o8+bNSzNj3TVGmiwBFZGXLOOX2ZbhlrvYrly5Ir773e+KgQMHivbt24sePXqI22+/XfzjH/+QcePcp08feRw+fFj069dPDBs2TF675ZZbZP2XvvSlGkZYLd73vveJ173udWLw4MFi+/btss3w4cNlGyRT2cPzHsrEiRNl3X333SemTp0q/XjHO94h1q5dW7P73HPPic9//vOiV69eom3btuLtb3+7fO7Cc6MqSWLDmNddd13ttrFTp041H5Qvjz32mDIjNm/eLNu//vWvFx/96EfFt771Ldn+C1/4gmzzzW9+U34fM2ZMrc/Xv/51WTd+/HhZt2fPHvkdz4a7du0Sb3vb28TXvvY1ee1f//qXxPiaa64Rb3jDGwRWFDwvNVoYaXTspuUF/n/oQx+SuA8YMED89re/FQ8++KBATpFnPE789a9/rQ1zzz33iP79+4s3vvGN8hg9erT43e9+V7uOD4wnaJM3TnUOCCH/b3ThuuD33MWGDQI8u7z0pS+VQgKR8f3666+Xq9aLL75YI+m73vUu+RmkRgmT+9ixY+KVr3ylbPOyl71MPh/BLuxdffXVss9///vfmr3169fLOggdbV772tfWruE7jv3798s258+fl8lGEkFo3IbiOgStStgfVY8xX/3qV9dsv/zlL5ffla+wg4kEBROPGhtYIA4Vwyc+8QnZBqJDm86dO6shxOc+9zlZ17NnT1n305/+VH5H3Oo58atf/aq8ZQVh0R+xQLD4DNJi86aRkofY0vIC7F7ykpdIP+Hrm9/8ZolfsA6TpCrvf//75aSNPAEP9MFEfubMGdlEhye4tc8bJ+WfOjPcchUbZnNFJMzWKJhxAA6ODRs2iGASQL6VK1fKmQ1tw+SePHmy7AchnDhxQkCoakXBSoQStKfEpuyg3x/+8Afxm9/8puYXCKoKkoWVGLMofFN+PvHEE7KJspO0QaLar1ixQrb/1a9+VbOhxPaWt7xF1mF1/tvf/iaAkRLqpz71KdlPR2y/+MUvaraxgmG1hK0tW7bIetwhXL58WdoDKeEbnoEbKYw0OjbT8tKlSxfx9NNPi1WrVtViwoqNu40JEybIOqzQqihR/f3vf5crGiY3xKee7XV4UgROyj91ZrjlKjZskSsCPvXUU8oHAXBR/5nPfKZOHPPnz6+1wYcwubt27Sr7BWc5RUwdsU2aNKlmv3fv3tIWblVV+fa3v13zTfmN80MPPSSbhP1R/dRZ9UkS26lTp2p4QMyqvOc975H1jYpt9+7dypTEFH5gdcDKhuOtb32rtD9lypRauywfGGl0bKWJbdasWdIEJjmF4c6dO2XdD37wg1rdv//9b1n3y1/+Urz3ve+t1as+d911l7yuwxNwL2+c5OCB/zDcchXbd77znRogJ0+erLmhkj9z5sw6samVSDUMk1v1A1CqZBFbcEUaNGiQ9E0JF7uHAP9Vr3qVWLBggYAvKon79u2Tw4X9UT6os2qfJLbjx4/XbG7dulV1E2Gx4bc82ArO5uHbyODKBruqQFDoi9uqbt261R233XabapbpzEijYyxNbIgN5Z///GcNHzzHofz4xz+u1b3wwgvi6NGjMkeIERMlntmx+4vvixYtkn10eFIETnLwwH8YbrmKDQ+6AAEHfhBGwXa8qsMGRVwSlL9hcuNBH30BLu7LAf673/1uWaezsqWJbdy4cdIOfohGCd7u4mEdJeyPrAz8R8WVJDZsEqjnRjx3nD17VsYRvo3ELbeydfDgQflsq54v1DNbktgwu6MvcMEGQB6FkUZnjLg8KzyziG358uUyPjyDouBRAhsliHnx4sWyTocnReAUxoHhlqvYMLj6YRoPux/84AflJgSAwWYIyBCXBOW0SoYSCZ6B1EMzngVBXPUdu4socfbCdtAuvLJNnz5dJgw2b731Vrm7pwiPnT+UODvywv//o9oniQ3NsKuo2mEsxKFiULeR2LRRbV7xilfIW0L17IvVCiVJbNgEUeTDDI9nHkwgEGnWN3H+HxbdVVPt0s5peckiNvWsBXxuvvnm2iYHvuOOBEWHJ0XgFI6/dLHhIXbGjBm1XUSQBslXrzDFJUE5HUfun//853Lr/53vfKcUxbRp0yQxsSGAEmcvzk5YbE8++WRtswU7hPh5As89SKK6pYmzo3zFWQkkTWzYgMEmUN++fQU2Nr7xjW8I9fyI20dVvvzlL9dECKGsWbNG2le7rkliQ39sxowYMaK2CQS/sLOJzaFGCiONjs20vGQRG17Bw085Cmts++MuAd/nzp1bc4XxBA3zxqk2+P8/MNxyX9mUAwDpj3/8o1z2VV0j5+DbGPiM37QANGa5PAo2MdSDeB72wjYgNhyq4HZYEQeCChb8BvnnP/+5tqsYvKbz+T//+Y+c1M6dO6fTPLENI01ixwIvYEcSt+FJJQtP8sIp7AvDrTCxhR1p5DueefDjLTY15syZIx/+FVHVJkYjdsvsg1vE7t27y9Uet6vqlg8/S6SRp0wfw2Mx0oTbV/3dFJ4w3IwWG1YBtZmgRIa3MPD7jC0FvwWpZzQVA24TsZ1tamGkMc1vU3jCcDNabEgqtofxuxeeo7BK4Ltt5S9/+YvAb2P4M6ADBw4Y/6IyI42J+JvAE4ab8WIzMbGu+8RI43r8jcbHcPNiaxRZh/sx0jgcelOhMdy82JqC183OjDRuRt18VAw3L7bmMXbOAiONcwHnFBDDzYstJ6BdMsNI41KsecbCcPNiyxNtR2wx0jgSZu5hMNy82HKH3H6DjDT2R1hMBAw3L7ZicLfaKiON1cEV6DzDzYutQPBtNc1IY2tcRfvNcPNiKzoDFtpnpLEwpFJcZrh5sZWSBrsGYaSxK5ryvGW4ebGVlwtrRmKksSaQkh1luHmxlZwQG4ZjpLEhhip8ZLilig2d/eEx8BzQ50CayBPFVuRfL6c55K9Vj4DPfWM5YLh5sTWGq9O9GGmcDr6J4BhuXmxNgOtqV0YaV+NuNi6Gmxdbswg72J+RxsGQcwmJ4ebFlgvMbhlhpHEr2vyiYbh5seWHtTOWGGmcCTTnQBhuXmw5A+6COUYaF2IsIgaGmxdbEahbbpORxvLwCnOf4ebFVhj09hpmpLE3smI9Z7h5sRWLv5XWGWmsDKoEpxluXmwlJMG2IRhpbIunLH8Zbl5sZWXConEYaSwKpVRXGW5ebKWmw47BGGnsiKJ8LxluXmzl58T4ERlpjA+gIgcZbl5sFSXG5GEZaUz2vUrfGG5ebFVmx9CxGWkMdbtytxhuXmyVp8g8BxhpzPPYDI8Ybl5sZuTJKC8YaYxy1iBnGG5ebAYlyxRXGGlM8dM0Pxhuzort8uXLYuHChaXnA/+UL8a2uTDSZI0NeCxatChrt8LaF5UjhpuTYkNyFyxYIKZPn15L2BNPPCGuXLlS+44P4e91Fxv8Mnv2bLF48WKrBcdIkwWauFyo/pcuXZL/5HHZk1NROWK4OSk2/PvbvXr1qiM8/k3rG2+8Uc6wmGXHjx8vrr76arFv3z6Ve3qGOEGMU6dOyVUzbrY+f/686N69u9iyZQu1Z2oDRposfsflAiJbsWKF6NOnj2jXrp0YMmSI2Lt3b12+sowRbFtljhhuzont4sWLYuTIkfIfig8m4d577xW4fQgeqMuyuk2aNEn2Hz16tDzHiQ1jbt26VfTr18/4f6g+iE/wMyNNsG3a57hcAG/c3gO7M2fOiAceeEBMmTJF4rlx48Y0c1rXqswRw805sa1bt05MnDgxMktCWEjynj17xOHDh8Vzzz2nlbxgI6xqOEAUiDZJbCDU2LFjxdq1a4PdrfnMSKMbSFwusKr17t1b5kLdPu7YsUPiOWzYMAGBNlOqzBHDzSmxgeSDBw8WGzZsiOQLYps/f36kvpEKJjbYnDlzppgxY0ZE9I2MV3YfRhodf5CL4cOHR3IBsQ0cOFAe+IwCgXTr1k20b9++abEp36rIEcPNKbHhtgQrzv79+xXmtTPEdtttt4lNmzYJ3GogGS+88ELtepYPOolcunSpvJ1Vs3cW+1W3ZaTR8Q9C6ty5c2wujh8/LnCocuHCBZm3vn375jY5VZEjhptTYsMtIsQWTKRKKMSGa5hBf/SjH4lp06aJQYMGiSeffFI10T7rJHLnzp2iQ4cOuc3U2s7l0JCRRmcI2EjKRbj/5s2bZdu4O5JwW93vWXIEsedRGG5OiQ07jkjw2bNnI9hBYBCcKs8884xsi6RkXX10Enns2DFp//Tp02pIa86MNDqBnDhxIjEXwf7Y2cUz3Ny5czPnIWgn/LmKHDHcnBSbzkM2nim6dOki+vfvn3n10UkkbqMgfEwAthVGGp141MSXlgtMcrilx+6xen5jttFu3rx5kSM8ThU5Yrg5JTasInErGxI0atQoceutt9blcsCAAbJ9OFF1jWK+6CRSrWyY4W0rjDQ68STlQvWF0LCJtGzZMrmiYfLDiwg4pxXkEr/LBQ88DoRzWEWOGG5OiQ333nhOCj+zIUEdO3aUO2AqmTi3bdtWrmy4rorOj6s6icQzG4TPEqDGNemch89JuUCcEBpWs/Xr19eEhhz06NGj7lYyLhfom3QEMawiRww3p8SGhCGJ4d1IJOfOO++UbymohOAZDmLALYkq27dvl3Xbtm2LnWEhUBzBRGJM2A8X7EZiNy7uWritad8ZaXT8TcqFwg93Fddcc43o2bOnfOOma9eu8mcbhRfLRZIPVeaI4eaU2JAo/LaFGTNc8KYCXqOaNWuWbAOhrVq1qk4M+FkA9VOnTo19hsCP4hAzXgVDO3WgDkkOFtwi4XemcH2wjamfGWl0/E7KBeoVbuHziBEjanixXCT5UGWOGG5OiQ0JwFsL48aNqxORSszBgwfFmjVr5G9tcS8mox3u/ZN+jIZw1EqGdiAOjrCg8H3MmDHSFzW2TWdGGt1YknKhcIs7B22n5SLYLvi5yhwx3JwTG8SAh+eTJ08Gc6D9GTMj3gpvpuChf+jQoZGH9mZsltmXkUbXFxNykeRrETliuDknNoC7evVqebuHmTNLATnwFsO5c+eydKtrC8Cx8YK33W0tjDRZ4qoyF0l+FpUjhpuTYoNo5syZI7eVkwCPq3/00UflS8px13Tr8Dd0WB2zCl3XfhntGGmy+NBoLvDTCV4YL6IUlSOGm5NiQ4JAdpC+7IKHfpuFBrwYabJiWlUukvwsKkcMN2fFlgS0r+cIMNJwC63ZguHmxdaavEiNmpEmtXMLX2S4ebG1MDmSQmekSerX6vUMNy+2VmdITPyMNDFdfJXGs64Xm6dJBAEvtggkWhUMNy82LRhbqxEjTWuhoR8tw82LTR/LlmnJSNMyQGQMlOHmxZYR0FZozkjTChg0EiPDzYutEVQd78NI43j4DYfHcPNiaxhadzsy0rgbeXORMdy82JrD18nejDROBp1DUAw3L7YcQHbNBCONa/HmFQ/DzYstL6QdssNI41CouYbCcPNiyxVuN4wx0rgRZf5RMNy82PLH3HqLjDTWB1hQAAw3L7aCgLfZLCONzbEV6TvDzYutSPQttc1IY2lYhbvNcEsVGzr7w2PgOaDPgTRFp4otraO/5i4CbIZ2N/LmImO4ebE1h6+TvRlpnAw6h6AYbl5sOYDsmglGGtfizSsehpsXW15IO2SHkcahUHMNheHmxZYr3G4YY6RxI8r8o2C4ebHlj7n1FhlprA+woAAYbl5sBQFvs1lGGptjK9J3hpsXW5HoW2qbkcbSsAp3m+HmxVZ4CuwbgJHGvojK8Zjh5sVWTh6sGoWRxqpgSnSW4ebFVmIybBmKkcaWOMr2k+HmxVZ2RiwYj5HGghAqcZHh5sVWSVrMHpSRxmzvq/OO4ebFVl1ujB2ZkcZYxyt2jOHmxVZxgkwcnpHGRJ9N8Inh5sVmQpYM84GRxjB3jXGH4ebFZkyqzHGEkcYcT83yhOHmxWZWvozwhpHGCCcNdILh5sVmYNKqdomRpmr/TB2f4eaU2C5fviwWLVpkTC7atGkj4JNthZFGJx7TcpHk8+LFi3PLEcPNGbEhuQsWLBDTp09PwjVSf+nSJQl0HoKAjb1799aNMXv2bJFnMuuMF/iFkYYN3UguYBP5UDlhYzRyvegcMdycEduuXbtEr169tGYpgH7zzTcLrDw4PvCBD4jDhw9r9Y1L8pUrV8SqVavEyJEjBT6rcv78edG9e3exZcsWVWXFmZGGBZElF7CFfAC/du3ayXyMHz9e7Nu3jw2T6XoZOWK4OSG2ixcvSqIfOHBAKwH33XefvN3ELIokzJw5Uyb517/+tVb/cKODBw/K8cNiQ7utW7eKfv36yRk73M/U74w0aX5nzQXwv/vuu8WHP/xhceLECXH69Glxyy23iLvuuittmMzXysgRw80Jsa1bt05MnDhRe2UaNWqUFJe67XvwwQfld9QHVyadjGJWxtgjRoyIrGzoD3tjx44Va9eu1TFnRBtGmjQns+biJz/5icT+4YcflmaPHDkievfuLebNm5c2TKZrZeWI4Wa92EDm4cOHiw0bNmgn4P777xczZswQmIVRvvKVr8iE43Yvq9hWrlwpli9fnriywT5WToyHpNtQGGmSYsiaC+CB3Kk7AnyHjbyf28rKEcPNerEhMZ07dxb79+9P4kBq/dmzZ8UNN9wgZ9Nnn302tW344qFDh8RNN90kyQHCKNKE2y1dulRec11sWXPx9NNPy0kOuG3fvl3gzmLatGni3nvvzTzphTFX38vMkfNiQ4DY5Dh+/LjCV+sM4s+fP19cf/31YsqUKeLo0aNa/VQj9J88ebLAcyJm4zSx7dy5U3To0EFcuHBBdTf6zEiT5HzWXPz+97+XuYPIFi5cKFd+3NpfddVV4mc/+1nSMNr1jeRI3e1oDxJoyHCzfmXDQzXEhhUqa8FMjF3Ij3/842LQoEHiqaee0jaBZ5MlS5bI9kxsx44dkz7i4d+GwkiTFIPKxZkzZ5Ka1NVjQwq5w44tcoGCM8Q3ePDgpm+7y84Rw816se3evVsmLDgjIWF4wA4fwTbBrD/yyCPSxoQJE2pJD14Pf3788cfFtddeK9ti9sShVjZ8hviCBf6AVPDVhsJIkxRD1lw89thjEhdsLqmiJi7gxW7r0/JcRY4YbtaLDatFeGVDEoYMGVJ3YOWC2F588UWxZs0asX79epVfKRbYwKFzO4oND/wm1KlTJ9GzZ0+5tY/ZGAeIgx/Xg0WtbJj5bSiMNEkxqFwEV7a0XDz//PMS8759+9YmKDVxIRd79uxJGkrWp9muIkcMN+vFhucgPA8FRaJWm7gzfm9BIrt06VK7TTl16pSsQz1mRBTMsHh+gI1wQZKDB3xQKxsEHe6DZzbYZskIj1PV90b9zJoL4ATcOnbsWMNMrWz9+/ev7RYDh7hcxOU3WFd2jhhu1osNgCJhuruReC4D8bG5oQreVkAd3ipRQsHuGOq2bdtWm3VV++AZ5IAPPXr0kH6gP+qCBbuR2DFVtoPXTPzMSJPkc9ZcAKfvf//7EmfcUqIoLPG8pXDUzUWSXypHakIsKkcMN+vFBuDwG1bwtjAJdNSjPbaWhw4dKl/vuuOOO8R1110nn++Cz3SbNm2SJJg6daokQJJN7KIhiRCmOlAXLLilwe9JijzBayZ+ZqRJ8jlrLmAH4sJuMH5+wXukuBXHRNhILpL8KitHDDfrxQaAMQuOGzcu08qBJD/00EPynTw8S+F7uCDh7MdoECx4wE5QVPg8ZswY6WPYvqnfGWnS/G4kF8DogQcekK/Q4cUC4BkuOrkI91HfYb+MHDHcnBAbCI4NkZMnTyp8czljRsSb+82UZcuWyVU0OFM3Y6+Mvow0aT6YnIskv/PKEcPNCbEBxNWrV9eemZJAzVIP0mCX7Ny5c1m61bUF+G3bthV4C96mwkjDYjExF0k+55kjhpszYoM45syZIzBL5VHwRgleim2m4G/rsDrG3RY1Y7fovow0bHwTc5Hkc545Yrg5IzaACVKHNyeSQC6jHhsmtgkNuDDS6GBnWi6SfM7zj3sZbk6JLQlQX58NAUaabNZapzXDzYutdbigHSkjjbahFmvIcPNiazFC6ITLSKNjoxXbMNy82FqRFSRmRhrSvWUvM9y82FqWGsmBM9Ik92ztKww3L7bW5kds9Iw0sZ18Jd3F9WLzJIkg4MUWgUSrguHmxaYFY2s1YqRpLTT0o2W4ebHpY9kyLRlpWgaIjIEy3LzYMgLaCs0ZaVoBg0ZiZLh5sTWCquN9GGkcD7/h8BhuXmwNQ+tuR0YadyNvLjKGmxdbc/g62ZuRxsmgcwiK4ebFlgPIrplgpHEt3rziYbh5seWFtEN2GGkcCjXXUBhuXmy5wu2GMUYaN6LMPwqGmxdb/phbb5GRxvoACwqA4ZYqNnT2h8fAc0CfA2k6ThVbWkd/zV0E2AztbuTNRcZw82JrDl8nezPSOBl0DkEx3LzYcgDZNROMNK7Fm1c8DDcvtryQdsgOI41DoeYaCsPNiy1XuN0wxkjjRpT5R8Fw82LLH3PrLTLSWB9gQQEw3LzYCgLeZrOMNDbHVqTvDDcvtiLRt9Q2I42lYRXuNsPNi63wFNg3ACONfRGV4zHDzYutnDxYNQojjVXBlOgsw82LrcRk2DIUI40tcZTtJ8PNi63sjFgwHiONBSFU4iLDzYutkrSYPSgjjdneV+cdw82LrbrcGDsyI42xjlfsGMPNi63iBJk4PCONiT6b4BPDzYvNhCwZ5gMjjWHuGuMOw82LzZhUmeMII405nprlCcPNi82sfBnhDSONEU4a6ATDzYvNwKRV7RIjTdX+mTo+w80psV2+fFksWrTImFy0adNGwCfbCiNN1nhMy8vixYsLyQvDzRmxIaELFiwQ06dPz8qFptpfunRJ4IgT1ezZs0VRiW3KadKZkYZ0r7vcSF7SMK0znvIlzUZReWG4OSO2Xbt2iV69etWR/sqVK/L7qVOnxMKFC3Nd9ZDMe+65R/Tp00e0a9dODBkyROzdu1dgTFXOnz8vunfvLrZs2aKqrDgz0mQJIi4vSf2B6YoVKyKYxk1kaTaqygvDzQmxXbx4UYwcOVIcOHCgLgeTJk0SuJUbPXq0POd1iwlBwS5myDNnzogHHnhATJkyRdZt3LixzoetW7eKfv36ydWv7oLBXxhpdF1Pyktcf2CqJkSGaVx/1FWdF4abE2Jbt26dmDhxYt2qBvAxI+KAyCCOvMSGGRj2Zs6cWRtzx44dsm7YsGECJFMFBBg7dqxYu3atqjL+zEijG0BSXuL6A9PevXtLwamVLAnTuP6oqzovDDfrxQYyDx8+XGzYsCEpB4WIbeDAgQIHEowCgnTr1k20b9++Tmy4BlHOmDGjJsxERw25wEij46ZOXoJ2gGMWTIN91eesNvLOC8PNerEB4M6dO4v9+/crzCPnvFc2DHD8+HF5qMEuXLggV7a+fftGRLV06VJ5m6tmbNXH1DMjjY7fOnkJ28mCabiv+p7FRt55YbhZLzYEiFs6gJxUihBbeCxsgsCPuBV2586dokOHDgKCtKEw0ujEoJMXZmfz5s2JmLK+6nqZeWG4WS+2EydOyIScPXtW4Rs5Fy027HbieWPu3LmRVQ3OHDt2TPp4+vTpiG8mVjDS6Pisk5c0OwzTtL7qGrORd14YbtaLbffu3ZLIwU0JBbY6NyI23AbNmzcvcoTHwa0hdj2xG4o+cQX1WPXgqw2FkUYnhri85Ikp86GKvDDcrBcbVgsQOe+VDcTAb2fBY9CgQXWbH0goHrKXLVsmVzRsCuCHdZyDRc2gmO1tKIw0OjHE5SVPTNN8qCovDDfrxYbnIDwPNfPMhh+jkaBgwfekA+1wDavZ+vXra0IDmXr06BGxhWc2TAgsGcHxq/ych59xeUnCE/W6mGIii8uXwqvKvDDcrBcbCA7Sx+1GIjE4greRaK+SiwRt375dCmHbtm2RFUklMHxWNgcMGCCuueYa0bNnT/mmCLb+Bw8eXGcffbHrhR3T4LhhmyZ9Z6TR8TUtL3H9gemnP/1pEca0a9euElN1+6rkQ3sAAAnXSURBVJ6WryQbZeWF4Wa92EBg/IaFFSZc8EYChIjXuLCyqAN1SAzKpk2bZP3UqVMTn7nCdkEkZSt8HjFiRM226odbTfwWqMZU9aaeGWl0/E7LS1x/tA9jqb4HMU3LV9V5YbhZLzYkDm8qjBs3LrJygNxqJcPMiITiCJMe17L86Iz+ylbcOUgmtB0zZoz0MVhv8mdGGl3fk/KS1D8OS1UX7JOUr6rzwnBzQmwQFDYyTp48GcyJ9mesgHjPsYiCzZOhQ4fWbawUMU6eNhlpdMdqNi9J4+SRryLywnBzQmxIyurVq+UtI2bCLAWEwFsf586dy9JNqy3Ab9u2rcCb7zYVRpossTSal6Qx8shXUXlhuDkjNiRhzpw5chs+KVFx9diWP3z4cNylpuvwt3WYhbNOAE0P3KQBRpos5hvNS9IYR48eFUeOHEm6rFVfVF4Ybs6IDSiD1CC3KQUP+LYJDdgx0mTF17S8FPUHvQw3p8SWlQS+fTwCjDTxvXwtw82LzXMkggAjTaSDr5AIMNy82DxRIggw0kQ6+AqJAMPNi80TJYIAI02kg6+QCDDcvNg8USIIMNJEOvgKiQDDzYvNEyWCACNNpIOvkAgw3LzYPFEiCDDSRDr4CokAw82LzRMlggAjTaSDr5AIMNy82DxRIggw0kQ6+AqJAMPNi80TJYIAI02kg6+QCDDcvNg8USIIMNJEOvgKiQDDzYvNEyWCACNNpIOvkAgw3LzYPFEiCDDSRDr4CokAw82LzRMlggAjTaSDr5AIMNy82DxRIggw0kQ6+AqJAMPNi80TJYIAI02kg6+QCDDcvNg8USIIMNJEOvgKiQDDLVVs6OwPj4HngD4H0uadVLGldfTX3EWAzdDuRt5cZAw3L7bm8HWyNyONk0HnEBTDzYstB5BdM8FI41q8ecXDcPNiywtph+ww0jgUaq6hMNy82HKF2w1jjDRuRJl/FAw3L7b8MbfeIiON9QEWFADDzYutIOBtNstIY3NsRfrOcPNiKxJ9S20z0lgaVuFuM9y82ApPgX0DMNLYF1E5HjPcvNjKyYNVozDSWBVMic4y3LzYSkyGLUMx0tgSR9l+Mty82MrOiAXjMdJYEEIlLjLcvNgqSYvZgzLSmO19dd4x3LzYqsuNsSMz0hjreMWOMdy82CpOkInDM9KY6LMJPjHcvNhMyJJhPjDSGOauMe4w3LzYjEmVOY4w0pjjqVmeMNy82MzKlxHeMNIY4aSBTjDcvNgMTFrVLjHSVO2fqeMz3KwX2+XLl8WiRYtMxb/mV5s2bQR8taEw0mSNwbQcFZULhpvVYkMSFyxYIKZPn541/4W2h1979+6tG2P27Nli8eLFVgiOkaYuMPKlmRzF4UiGi1yOs1FULhhuVott165dolevXloEvnLlimx36tQpsXDhwsJWQ4yzatUqMXLkSIHPqpw/f150795dbNmyRVUZe2akyeJ4lhyF7SocIZhGStm5YLhZK7aLFy9KQh84cEArD5MmTRK4fejcubM8F3XrefDgQelXWGxwcuvWraJfv37i0qVLWj5X1YiRRtevrDkK2g3i2KjYgjaCEx/GKSIXDDdrxbZu3ToxceJErVUN4CJhOKZNm1aY2GAfPo0YMSKyssEHJHzs2LFi7dq1QV4Z95mRRtfhrDlSdsM44nvWErYRFlsRuWC4WSk2ADV8+HCxYcOGrDkQs2bNKkxsK1euFMuXL09c2eDszJkzxYwZM7QnicwB5tCBkUZniGZyFMaxEbGFbYTFVkQuGG5Wig23Ybgd3L9/v07e69rcfvvthYjt0KFD4qabbpK3iLiFjLuNhCNLly6V1xohUF0gBX5hpNEZutEcAccJEybU4ZgVq6pywXCzUmwICs9fx48f18l7XZsvfvGLuYsNZJg8ebLA8yNm0DSx7dy5U3To0EHgecbUwkij43cjOUrCMYvYkmzErWwqFxcuXNAJibZhuFkpthMnTkjBnDlzhgIQbjB//vzcxYZnkyVLlsihmNiOHTsmxz99+nTYNWO+M9LoOKpydPbsWZ3mso3CERgGccwiNmUDBoM28Dlc8s4Fw81Kse3evVsSNrg64LZl3rx5kSPYBmBjFxKrYpbdyDTbjz/+uLj22mvlbQ9IgUOtbPgcTjJsYXzEYGphpNHxO2uO0nAEZmEc43xIs1FGLhhuVooNqwIIG1zZkJAhQ4bUHYMGDYrcrjUqtiTb2PBo166d6NSpk+jZs6fc2h81apTAgV1J/OgeLGo2xcxvamGk0fFb5Si4sqXlKCuOcT5ktZF3LhhuVooN99h47gk+s6lVJe4cTAwTG978gI1gibMZrAOJ1AHf1MqGVTVsC88JmChYYoLjl/05D9+y5gg4KQxxBnZxOGKFi8sRMAr2x+eyc8Fws1JsABKJyLIbiSThCIoNdoJi2L59uxTCtm3btG5bwiKAfeUb/INt1AULdiOxkxocN3jdhM+MNDo+Khyy5EjZTcNRN0fKRo8ePSRXysgFw81KsQE4/Fa1fv16lR96xitaEABe78LKog7UKUFs2rRJ1k+dOlWKhhoNNVBjKNs4oy5YcKuD3wjVmMFrpnxmpNHxs5EcKbtpOOrmKM2GGifvXDDcrBQbwMKu07hx47RXCDXTgQTq9i5utsO1Rn90xhiwqQ7M7kFR4fOYMWOk7yrhJp4ZaXR9zpojZZfhqJMjlQN1LiMXDDdrxQbwsGlx8uRJlaNczpgR8VZ4EWXZsmVi6NChkU2bIsZqxiYjja5tk3NURC4YbtaKDQlfvXp17X5clwBp7UCOvn37inPnzqU1a+gaEtG2bVuBt+BNL4w0Wfw3MUdF5YLhZrXYII45c+YIzFJ5lKNHj4ojR47kYSpiA39zh1UTtzWmF0aaLP6bmKOicsFws1psSDrICxKbXrBZYoPQgCMjTVasTctRUblguFkvtqyJ9+05Aow03EJrtmC4ebG1Ji9So2akSe3cwhcZbl5sLUyOpNAZaZL6tXo9w82LrdUZEhM/I01MF1+l8azrxeZpEkHAiy0CiVYFw82LTQvG1mrESNNaaOhHy3DzYtPHsmVaMtK0DBAZA2W4ebFlBLQVmjPStAIGjcTIcPNiawRVx/sw0jgefsPhMdy82BqG1t2OjDTuRt5cZAw3L7bm8HWyNyONk0HnEBTDzYstB5BdM8FI41q8ecXDcPNiywtph+ww0jgUaq6hMNy82HKF2w1jjDRuRJl/FAw3L7b8MbfeIiON9QEWFADDzYutIOBtNstIY3NsRfrOcPNiKxJ9S20z0lgaVuFuM9xSxYbO/vAYeA7ocyBN0YliS+vkr3kEPALZEfBiy46Z7+ERaAgBL7aGYPOdPALZEfBiy46Z7+ERaAiB/wFGUWmH10yu7AAAAABJRU5ErkJggg==[/img][br]
[size=150]Select [b]all [/b]the transformations that produce congruent images.[/size]
Here are some transformation rules.
[size=150]For each transformation, first predict what the image of triangle ABC will look like. Then compute the coordinates of the image and draw it.[/size]
(x,y)→(x-4,y-1)
(x,y)→(y,x)
(x,y)→(1.5x,1.5y)
A cylinder has radius 3 inches and height 5 inches. A cone has the same radius and height. An applet is provided below to help you answer the following questions.
Find the volume of the cylinder.[br]
Find the volume of the cone.[br]
What fraction of the cylinder’s volume is the cone’s volume?[br]
[size=150]Reflect triangle [math]ABC[/math] over the line [math]x=-2[/math]. Call this new triangle [math]A'B'C'[/math]. Then reflect triangle [math]A'B'C'[/math] over the line [math]x=0[/math]. Call the resulting triangle [math]A''B''C''[/math].[/size][br][br]Describe a single transformation that takes [math]ABC[/math] to [math]A''B''C''[/math].
In the construction, A is the center of one circle, and B is the center of the other.
[img]data:image/png;base64,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[/img][br][br]Explain why segments [math]AC[/math], [math]BC[/math], [math]AD[/math], [math]BD[/math], and [math]AB[/math] have the same length.

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