Look at the diagram below. A is the center of dilation. Triangle XYZ is the preimage and Triangle X'Y'Z is the image. Drag Point A to move the center of dilation, drag points X, Y, or Z to change the shape of the triangle, and adjust the slider to change the scale factor. You can show or hide the lines from the center of dilation and various measures.
Change the slider to a value greater than 1.
1. Is triangle X'Y'Z larger or smaller than triangle XYZ?
2. Is it closer to Point A or farther from point A than triangle XYZ?
3. Is it on the same side of point A as triangle XYZ, between point A and triangle XYZ, or on the opposite side of point A?
Now, change the slider to a value between 0 and 1.
4. Is triangle X'Y'Z larger or smaller than triangle XYZ?
5. Is it closer to Point A or farther from point A than triangle XYZ?
6. Is it on the same side of point A as triangle XYZ, between point A and triangle XYZ, or on the opposite side of point A?
Now, change the slider to a value between 0 and -1.
7. Is triangle X'Y'Z larger or smaller than triangle XYZ?
8. Is it closer to Point A or farther from point A than triangle XYZ?
9. Is it on the same side of point A as triangle XYZ, between point A and triangle XYZ, or on the opposite side of point A?
Now, change the slider to a value less than -1.
10. Is triangle X'Y'Z larger or smaller than triangle XYZ?
11. Is it closer to Point A or farther from point A than triangle XYZ?
12. Is it on the same side of point A as triangle XYZ, between point A and triangle XYZ, or on the opposite side of point A?
13. Change the value of the scale factor to 1. What happens?
14. Change the value of the scale factor to -1. What happens? What other transformation would get this result?
15. Change the value of the scale factor to 0. What happens?