# Lesson 3

Measuring Dilations

### Problem 1

Pentagon $$A’B’C’D’E’$$ is the image of pentagon $$ABCDE$$ after a dilation centered at $$F$$. What is the scale factor of this dilation?

### Problem 2

A polygon has perimeter 12 units. It is dilated with a scale factor of $$\frac{3}{4}$$. What is the perimeter of its image?

A:

9 units

B:

12 units

C:

16 units

D:

It cannot be determined.

### Problem 3

Triangle $$ABC$$ is taken to triangle $$A’B’C’$$ by a dilation. Which of these scale factors for the dilation would result in an image that was larger than the original figure?

A:

$$\frac{3}{5}$$

B:

$$\frac{13}{17}$$

C:

1

D:

$$\frac{4}{3}$$

### Problem 4

Dilate quadrilateral $$ABCD$$ using center $$D$$ and scale factor 2.

### Solution

(From Unit 3, Lesson 2.)

### Problem 5

Dilate Figure $$G$$ using center $$B$$ and scale factor 3.

### Solution

(From Unit 3, Lesson 2.)

### Problem 6

Polygon Q is a scaled copy of Polygon P.

The value of $$x$$ is 6, what is the scale factor?

A:

$$\frac34$$

B:

$$\frac43$$

C:

3

D:

4

### Solution

Prove that segment $$AD$$ is congruent to segment $$BC$$