[color=#000000]In the applet below, the [/color][color=#ff0000][b]red segment (with endpoints [i]B & C[/i])[/b][/color][color=#000000] [/color][color=#ff0000][b]"preimage"[/b][/color][color=#000000] has been dilated about the [/color][b]black point [i]O. [/i][/b][color=#000000] The image of this segment has endpoints [/color][i][color=#ff0000]B'[/color] [/i][color=#000000]and [/color][i][color=#ff0000]C'[/color][/i][i]. [/i][color=#000000]The [/color][i][color=#980000][b]scale factor[/b][/color][/i][color=#000000] of the dilation is given by the parameter [/color][color=#980000][b][i]k[/i].[/b][/color][color=#000000] (See below.) [/color][i] [br][br][/i][color=#000000]At any time, feel free to change the locations of point [/color][color=#ff0000][b][i]B, C, [/i][/b][/color][color=#000000]and/or [/color][i][b]O[/b][/i][color=#000000]. Also, feel free to adjust the [/color][b][color=#980000]scale factor[/color][/b][color=#000000] using the [/color][color=#980000][b]slider[/b][/color][color=#000000]. [br][/color][br][color=#000000]Select the "Check This Out!" box. Interact with the elements you see there. As you continue to interact with this applet, pay very close attention to the length and position of the image segment with respect to the preimage segment. [/color][br][br][color=#000000]Answer the questions that appear below the applet. [/color]
[color=#000000]1) The image of any segment under a dilation about a point is another ______________. [br][br][/color][color=#000000] [/color]
[color=#000000]2) What does the image look like if the scale factor [i]k = [/i]1? Describe. [br][br][/color]
[color=#000000]3) What does the image segment look like if the scale factor [i]k = [/i]0? Describe.[br][/color]
[color=#000000]4) What does the image segment look like if the scale factor [i]k = [/i]-1? Describe. [br][br][/color]
[color=#000000]5) What happens to the location of the image of the original segment if [i]k [/i]> 0 vs. [i]k [/i]< 0? [br][br][/color]
[color=#000000]6) Suppose the preimage has length = 4.8 cm. If [i]k [/i]= 3.2, determine the length[br] of the image of this segment. [br][br][/color]
[color=#000000]7) Suppose the image has a length of 12.5 cm. If [i]k[/i] = 1.5, determine the length of the [br] preimage. [br][br][/color]
[color=#000000]8) What does the action with the [/color][color=#0000ff]blue angles [/color][color=#000000]imply about the 2 segments? [/color]
[b][color=#274e13][i]Let's generalize now: Fill in the blanks to make a true statement: [/i][br][br]Suppose a ______________ is dilated about a ____________ with scale factor [i]k[/i]. [br][br]Then the ________________ of this original _____________ is another __________ [br][br]that is both _______________ to the original segment and has a ____________[br][br]that is ______ times as _______ as the original ________________. [/color][/b]
[b][color=#274e13]Suppose a __segment________ is dilated about a ____point________ with scale factor [i]k[/i]. [br][br]Then the _____image___________ of this original ____segment_________ is another _____segment_____ [br][br]that is both _____proportional__________ to the original segment and has a ____scale factor________[br][br]that is __k____ times as __big/small_____ as the original ____segment____________. [/color][/b]