# Measuring Dilations

ID: tozog-zifab
Illustrative Mathematics
Subject: Geometry

7 questions

# Measuring Dilations

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##### Problem 1

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

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) $\text{9 units}$b) $\text{12 units}$c) $\text{16 units}$d) $\text{It cannot be determined.}$
##### Problem 3

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) $\text{1}$d) $\frac{4}{3}$
##### Problem 4

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

##### Problem 5

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

##### Problem 6

6) Polygon ﻿$Q$﻿ is a scaled copy of Polygon ﻿$P$﻿. The value of ﻿$x$﻿ is 6. What is the scale factor?

a) $\frac{3}{4}$b) $\frac{4}{3}$c) $\text{3}$d) $\text{4}$
##### Problem 7

7) Prove that segment ﻿$AD$﻿ is congruent to segment ﻿$BC$﻿.