# 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?

### Solution

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### 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?

9 units

12 units

16 units

It cannot be determined.

### Solution

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### 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?

\(\frac{3}{5}\)

\(\frac{13}{17}\)

1

\(\frac{4}{3}\)

### Solution

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### Problem 4

Dilate quadrilateral \(ABCD\) using center \(D\) and scale factor 2.

### Solution

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(From Unit 3, Lesson 2.)### Problem 5

Dilate Figure \(G\) using center \(B\) and scale factor 3.

### Solution

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(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?

\(\frac34\)

\(\frac43\)

3

4

### Solution

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(From Unit 3, Lesson 1.)### Problem 7

Prove that segment \(AD\) is congruent to segment \(BC\).

### Solution

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(From Unit 2, Lesson 10.)