Determine the scale factor and the location of your center of dilation from triangle [i]ABC[/i] to triangle [i]A'B'C'[/i]. Adjust your scale factor, "k" using the slider, and adjust the location of the center of dilation, "P" until you have mapped triangle [i]ABC[/i] on to triangle [i]A'B'C'. [/i]

Determine the scale factor and the location of your center of dilation from polygon [i]ABCDE[/i] to polygon [i]A'B'C'D'E'[/i]. Adjust the scale factor, "k" using the slider, and adjust the location of the center of dilation, "P" until you have mapped polygon [i]ABCDE[/i] on to polygon [i]A'B'C'D'E'[/i].

Determine the scale factor and the location of your center of dilation from quadrilateral [i]ABCD[/i] to quadrilateral [i]A'B'C'D'[/i]. Adjust the scale factor, "k" using the slider, and adjust the location of the center of dilation, "P" until you have mapped triangle [i]ABC[/i] on to triangle [i]A'B'C'. [/i]

Determine the scale factor and the location of your center of dilation from triangle [i]ABC[/i] to triangle [i]DEF[/i]. Adjust the scale factor, "k" using the slider, and adjust the location of the center of dilation, "P" until you have mapped triangle [i]ABC[/i] on to triangle [i]DEF. [/i]

How does the center of dilation affect how a shape "dilates"? What happens when the point is away from the shape, in the middle of the shape, or on a vertex?[br][br]When the scale factor is greater than one, does the [i]image[/i] move closer to the center of dilation or further away?[br][br]When the scale factor is less than one, does the [i]image[/i] move closer to the center of dilation or further away?[br][br]Why were we unable to map triangle [i]ABC[/i] on to triangle [i]DEF[/i] in question 4? [br][br][br][br]

The scale factor from triangle [i]ABC[/i] to triangle [i]A'B'C' [/i]is equal to 1/3. Determine the location of the center of dilation. Use the ray tool [icon]/images/ggb/toolbar/mode_ray.png[/icon]to connect corresponding points starting with the larger image, then use the point tool[icon]/images/ggb/toolbar/mode_complexnumber.png[/icon] to mark where the rays intersect. Since our scale factor is less than one, our [i]image[/i] is smaller then our [i]preimage[/i], so you must draw your ray starting with one pre[i]image[/i] point and then selecting the corresponding [i]image[/i] point. For example, select the ray tool, [icon]https://www.geogebra.org/images/ggb/toolbar/mode_ray.png[/icon], then select [i]A[/i], and then select [i]A'. [/i]

The scale factor from quadrilateral [i]ABCD[/i] to quadrilateral [i]A'B'C'D [/i]is equal to 2.5. Determine the location of the center of dilation. Use the ray tool [icon]/images/ggb/toolbar/mode_ray.png[/icon]to connect two pairs of corresponding points starting with the larger image, then use the point tool[icon]/images/ggb/toolbar/mode_complexnumber.png[/icon] to mark where the rays intersect. Since our scale factor is greater than one, our [i]image [/i]is larger then our [i]preimage[/i], so you must draw your ray starting with one [i]image[/i] point and then selecting the corresponding [i]preimage[/i] point. For example, select the ray tool, [icon]https://www.geogebra.org/images/ggb/toolbar/mode_ray.png[/icon], then select [i]A'[/i], and then select [i]A. [/i]

Determine the scale factor from triangle [i]ABC[/i] to triangle [i]A'B'C'. [/i]Measure the distance from [i]A [/i]to [i]B [/i]by selecting the distance tool [icon]/images/ggb/toolbar/mode_distance.png[/icon], then select each point. Measure the distance from [i]A'[/i] to [i]B'. [/i][br]Measure the distance from [i]P[/i] to [i]B[/i] by first selecting the distance tool [icon]https://www.geogebra.org/images/ggb/toolbar/mode_distance.png[/icon], then click on [i]P[/i] followed by [i]B. [/i]Repeat this procedure to measure the distance from [i]P[/i] to [i]B'. [br][br][/i]Select the angle measure tool, and measure angle [i]BAC[/i] and angle [i]B'A'C'[/i]. Measure all other pairs of corresponding angles

Set up a ratio of side [i]A'B'[/i] divided by side AB. What is the scale factor from triangle [i]ABC[/i] to triangle [i]A'B'C? [br][br][/i]Set up a ratio of [i]P'B'[/i] divided by [i]PB. [/i]Does this ratio match your scale factor?[br][br]How do corresponding angles compare under a dilation? [br][br][br]

Determine the dilation that takes triangle [i]ABC[/i] to triangle [i]A'B'C'[/i]. Find your scale factor and center of dilation. Then, scroll down to 8b, and follow the appropriate directions

Using the scale factor and center of dilation found in 8a, plot your center of dilation using the point tool [icon]/images/ggb/toolbar/mode_complexnumber.png[/icon]and then dilate triangle [i]ABC. [/i]Select the dilate from point tool [icon]/images/ggb/toolbar/mode_dilatefrompoint.png[/icon], click on the inside of triangle [i]ABC[/i], then type in your scale factor. Check to make sure your dilated image matches triangle [i]A'B'C'[/i] in 8a.

Determine the dilation that takes quadrilateral [i]ABCD[/i] to quadrilateral [i]A'B'C'D'[/i]. Find your scale factor and center of dilation. Then, scroll down to 9b, and and follow the appropriate directions

Using the scale factor and center of dilation found in 9a, plot your center of dilation using the point tool [icon]/images/ggb/toolbar/mode_complexnumber.png[/icon]and then dilate quadrilateral [i]ABCD. [/i]Select the dilate from point tool [icon]/images/ggb/toolbar/mode_dilatefrompoint.png[/icon], click on the inside of quadrilateral [i]ABCD[/i], then type in your scale factor. Check to make sure your dilated image matches quadrilateral [i]A'B'C'D'[/i] in 9a.

In order to create a dilation that is dynamic like questions 1-4, follow the directions below. You still have a limited tool pallet; however you have access to all of the menus. [br][br]Create your own polygon using the polygon tool [icon]/images/ggb/toolbar/mode_polygon.png[/icon]. Then, using the point tool [icon]https://www.geogebra.org/images/ggb/toolbar/mode_complexnumber.png[/icon] , plot a point away from your polygon; this will serve as your center of dilation.[br][br]Select dilate from point tool, and when the dialogue box pops up for you to input your scale factor, type in the letter k instead of a number. You should see an option pop up that says "Create a slider for k"? Click "create sliders."[br][br]You will now see a slider up above. I recommend right clicking on it, and under "slider" adjust the minimum to zero (a negative dilation ends up inverting the image). [br][br]There are a whole host of menus to access simply by right clicking on various objects. Simple things such as adjusting the colors are fun to play with.