# Lesson 5: More Dilations

Let’s look at dilations in the coordinate plane.

## 5.1: Many Dilations of a Triangle

Explore the applet and observe the dilation of triangle $ABC$. The dilation always uses center $P$, but you can change the scale factor. What connections can you make between the scale factor and the dilated triangle?

GeoGebra Applet jjRtyeJX

## 5.2: Info Gap: Dilations

Your teacher will give you either a problem card or a data card. Do not show or read your card to your partner.

If your teacher gives you the problem card:

3. Explain to your partner how you are using the information to solve the problem.

If your teacher gives you the data card:

2. Ask your partner “What specific information do you need?” and wait for your partner to ask for information. Only give information that is on your card. (Do not figure out anything for your partner!)
3. Before telling your partner the information, ask “Why do you need that information?”
4. After your partner solves the problem, ask them to explain their reasoning and listen to their explanation.
One important use of coordinates is to communicate geometric information precisely. Let’s consider a quadrilateral $ABCD$ in the coordinate plane. Performing a dilation of $ABCD$ requires three vital pieces of information:
1. The coordinates of $A$, $B$, $C$, and $D$
2. The coordinates of the center of dilation, $P$
With this information, we can dilate the vertices $A$, $B$, $C$, and $D$ and then draw the corresponding segments to find the dilation of $ABCD$. Without coordinates, describing the location of the new points would likely require sharing a picture of the polygon and the center of dilation.