# Lesson 10

Dilations on a Square Grid

Let’s dilate figures on a square grid.

### Problem 1

Triangle $$ABC$$ is dilated using $$D$$ as the center of dilation with scale factor 2.

The image is triangle $$A’B’C’$$. Clare says the two triangles are congruent, because their angle measures are the same. Do you agree? Explain how you know.

### Problem 2

On graph paper, sketch the image of quadrilateral PQRS under the following dilations:

1. The dilation centered at $$R$$ with scale factor 2.
2. The dilation centered at $$O$$ with scale factor $$\frac{1}{2}$$.
3. The dilation centered at $$S$$ with scale factor $$\frac{1}{2}$$.

### Problem 3

Quadrilateral $$ABCD$$ is dilated with center $$(0,0)$$, taking $$B$$ to $$B'$$. Draw $$A'B'C'D'$$.

### Problem 4

Triangles $$B$$ and $$C$$ have been built by dilating Triangle $$A$$.

1. Find the center of dilation.
2. Triangle $$B$$ is a dilation of $$A$$ with approximately what scale factor?
3. Triangle $$A$$ is a dilation of $$B$$ with approximately what scale factor?
4. Triangle $$B$$ is a dilation of $$C$$ with approximately what scale factor?

### Problem 5

Here is a triangle.

1. Draw the dilation of triangle $$ABC$$, with center $$(0,0)$$, and scale factor 2. Label this triangle $$A’B’C’$$.
2. Draw the dilation of triangle $$ABC$$, with center $$(0,0)$$, and scale factor $$\frac{1}{2}$$. Label this triangle $$A’’B’’C’’$$.
3. Is $$A’’B’’C’’$$ a dilation of triangle $$A’B’C’$$? If yes, what are the center of dilation and the scale factor?

### Problem 6

The diagram shows three lines with some marked angle measures.

Find the missing angle measures marked with question marks.

(From Unit 1, Lesson 12.)