# How to "Make" a Dilation

- Author:
- David Hornbeck

- Topic:
- Dilation

You probably know how to dilate a pre-image to create an image; it's just a formula, right? What if you already have two triangles, though? Can you drag the vertices to "make" them dilations of each other?

1. Familiarize yourself with the sketch. There are no sliders. Figure out what the numbers in the top right represent. DO NOT CLICK ON THE HINTS UNTIL ASKED TO.
2. The sketch says that a dilation has occurred. Explain why this is true.
2b. Is ∆A'B'C' is a dilation of ∆ABC or is ∆ABC is a dilation of ∆A'B'C'? Justify.
3. Drag any of the vertices of the triangles. Try to create two triangles that are dilations of one another (you can’t use both of the original triangles). Follow these instructions:
If you successfully get two triangles, raise your hand to signal the teacher and await further instructions.
If you cannot get two triangles within five minutes, click “Hint 1.”
If you cannot get two triangles within 2 more minutes, click “Hint 2.”
If you cannot get two triangles within 2 more minutes, click “Hint 3.”
If you cannot get two triangles within 2 more minutes, signal the teacher if they have not already worked with you.
4. Describe how you created the triangles. What relationships had to hold in order for the two triangles to be dilations of each other?