8.GM.1 - Dilation Exploration

DIRECTIONS:
1) Select the slider tool to create a slider. [br] Name the slider [b]k[/b]. [br] Set Min = -5, Max = 5, Increment = 0.1[br][br]2) Select the DILATE FROM POINT [icon]/images/ggb/toolbar/mode_dilatefrompoint.png[/icon] tool. [br] Highlight a box around [b][color=#cc0000]point [i]A[/i][/color][/b], [color=#1e84cc][b]point [i]B[/i][/b][/color], and [b][color=#980000]Curious George's picture[/color][/b]. [br] Then select point [i]C[/i] (to serve as center of dilation)[br] In the pop-up box that appears, enter "k" (without the " " 's) to serve as the scale factor. [br][br]3) Select the Move tool. [b]Explore! [/b][br][br]Please answer the questions that appear below the applet.
1)
Suppose [b][color=#cc0000]point [i]A[/i] = (1, [i]2[/i])[/color][/b] is dilated about [b]C(0,0) [/b]with scale factor 2. [br]Suppose [b][color=#1e84cc]point [i]B[/i] = (4, 1)[/color][/b] is dilated about [b]C(0,0) [/b]with scale factor 2. [br][br]What would the coordinates of the [i]A'[/i] = image of [i]A[/i] be? [br]What would the coordinates of [i]B' = [/i]image of [i]B[/i] be?
2)
Suppose [b][color=#cc0000]point [i]A[/i] = (1, [i]2[/i])[/color][/b] is dilated about [b]C(0,0) [/b]with scale factor 3. [br]Suppose [b][color=#1e84cc]point [i]B[/i] = (4, 1)[/color][/b] is dilated about [b]C(0,0) [/b]with scale factor 3. [br][br]What would the coordinates of the [i]A'[/i] = image of [i]A[/i] be? [br]What would the coordinates of [i]B' = [/i]image of [i]B[/i] be?
3)
Suppose [b][color=#cc0000]point [i]A[/i] = (1, [i]2[/i])[/color][/b] is dilated about [b]C(0,0) [/b]with scale factor 4. [br]Suppose [b][color=#1e84cc]point [i]B[/i] = (4, 1)[/color][/b] is dilated about [b]C(0,0) [/b]with scale factor 4. [br][br]What would the coordinates of the [i]A'[/i] = image of [i]A[/i] be? [br]What would the coordinates of [i]B' = [/i]image of [i]B[/i] be?
4)
Suppose [b][color=#cc0000]point [i]A[/i] = (1, [i]2[/i])[/color][/b] is dilated about [b]C(0,0) [/b]with scale factor 0.5. [br]Suppose [b][color=#1e84cc]point [i]B[/i] = (4, 1)[/color][/b] is dilated about [b]C(0,0) [/b]with scale factor 0.5. [br][br]What would the coordinates of the [i]A'[/i] = image of [i]A[/i] be? [br]What would the coordinates of [i]B' = [/i]image of [i]B[/i] be?
5)
Suppose [b][color=#cc0000]point [i]A[/i] = (1, [i]2[/i])[/color][/b] is dilated about [b]C(0,0) [/b]with scale factor 0. [br]Suppose [b][color=#1e84cc]point [i]B[/i] = (4, 1)[/color][/b] is dilated about [b]C(0,0) [/b]with scale factor 0. [br][br]What would the coordinates of the [i]A'[/i] = image of [i]A[/i] be? [br]What would the coordinates of [i]B' = [/i]image of [i]B[/i] be?
5)
Suppose [b][color=#cc0000]point [i]A[/i] = (1, [i]2[/i])[/color][/b] is dilated about [b]C(0,0) [/b]with scale factor -1. [br]Suppose [b][color=#1e84cc]point [i]B[/i] = (4, 1)[/color][/b] is dilated about [b]C(0,0) [/b]with scale factor -1. [br][br]What would the coordinates of the [i]A'[/i] = image of [i]A[/i] be? [br]What would the coordinates of [i]B' = [/i]image of [i]B[/i] be?[br][br]What if the scale factor was -2? -3?
5)
What do you notice? Write any observation(s) you have below.
6)
Notice how the image of [b]f [/b]is called [b]f'[/b]. [br][br]How do their lengths compare? [br][br][b]When is f' bigger than f? [br]When is it smaller than f? [/b] [br][br][i]Be specific! [/i]
7)
Go to the STEPS window now (notebook-looking icon to the left of the circle/triangle symbol) [br]Hide the pictures of George and his image by de-selecting the bubbles of[b] pic1[/b] & [b]pic1'.[/b] [br][br]This should only leave the points and segments remaining. [br][br][br]What else can we conclude segments about f' and f? [i]Be sure to move points A and B around! [/i]
8)
Use the tool(s) provided to you to prove your conjecture for (7) is true. Can you also illustrate this another way?
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Information: 8.GM.1 - Dilation Exploration