Lesson 3

Measuring Dilations

  • Let’s dilate polygons.

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.

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.

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?









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.
(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.
(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?









(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.
(From Unit 2, Lesson 10.)