[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]
1) Fill in the blank: [br][br] The image of any segment under a dilation about a point is another ______________.
2) What does the image look like if the scale factor [i]k = [/i]1? Describe.
3) What does the image segment look like if the scale factor [i]k = [/i]0? Describe.[br]
4) What does the image segment look like if the scale factor [i]k = [/i]-1? Describe. [br]
5) What happens to the location of the image of the original segment if [i]k [/i]> 0 vs. [i]k [/i]< 0?
6) Suppose the preimage has length = 4.8 cm. If [i]k [/i]= 3.2, determine the length[br][br] of the image of this segment.[br]
7) Suppose the image has a length of 12.5 cm. If [i]k[/i] = 1.5, determine the length of the [br][br] preimage.
8) What does the action with the blue angles imply about the 2 segments? [br][br]
[b][i]Let's generalize now: Fill in the blanks to make a true statement: [/i][/b][br][br][b][/b][br][b]Suppose a _______[color=#0000ff](a)[/color]_______ is dilated about a ______[color=#0000ff](b)[/color]______ with scale factor [i]k[/i]. [/b][br][b][/b][br][b]Then the ________[color=#0000ff](c)[/color]________ of this original _______[color=#0000ff](d)[/color]______ is another _____[color=#0000ff](e)[/color]_____ [/b][br][b][/b][br][b]that is both _______[color=#0000ff](f)[/color]________ to the original segment and has a ______[color=#0000ff](g)[/color]______[/b][br][b][/b][br][b]that is ___[color=#0000ff](h)[/color]___ times as ____[color=#0000ff](i)[/color]___ as the original ________[color=#0000ff](j)[/color]________.[/b][br][br][br]