Lesson 3

Measuring Dilations

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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?

2 Pentagons.

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?

A:

9 units

B:

12 units

C:

16 units

D:

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?

A:

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

B:

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

C:

1

D:

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

Solution

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Problem 4

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

Quadrilateral A B C D on isometric grid. Side A B is 2 diagonal units long, side B C is 2 diagonal units long, and side C D is 3 diagonal units long.

Solution

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(From Unit 3, Lesson 2.)

Problem 5

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

Figure G has almost half of the top of a circle with three points The endpoints are connected to another point below and to the left of the half circle. Point B is to the left of figure G.

Solution

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(From Unit 3, Lesson 2.)

Problem 6

Polygon Q is a scaled copy of Polygon P.

2 4-sided polygons, P and Q. 1 side in polygon P is 4 and its corresponding side in Q is 3. Another side in polygon P is x, and its corresponding side in Q is y.

The value of \(x\) is 6, what is the scale factor?

A:

\(\frac34\)

B:

\(\frac43\)

C:

3

D:

4

Solution

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(From Unit 3, Lesson 1.)

Problem 7

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

Quadrilateral A B C D, with point E in the middle. Diagonals D B and A C drawn through E. Opposite sides are marked with arrows in the middle. Segments A E and E C have 1 tick mark.

Solution

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(From Unit 2, Lesson 10.)