Lesson 4

Dilations on a Square Grid

Problem 1

Triangle $$ABC$$ is dilated using $$D$$ as the center of dilation with scale factor 2.

The image is triangle $$A’B’C’$$. Clare says the two triangles are congruent, because their angle measures are the same. Do you agree? Explain how you know.

Problem 2

On graph paper, sketch the image of quadrilateral PQRS under the following dilations:

1. The dilation centered at $$R$$ with scale factor 2.
2. The dilation centered at $$O$$ with scale factor $$\frac{1}{2}$$.
3. The dilation centered at $$S$$ with scale factor $$\frac{1}{2}$$.

Problem 3

The diagram shows three lines with some marked angle measures.

Find the missing angle measures marked with question marks.

Solution

(From Unit 1, Lesson 14.)

Problem 4

Describe a sequence of translations, rotations, and reflections that takes Polygon P to Polygon Q.

Solution

Point $$B$$ has coordinates $$(\text-2,\text-5)$$. After a translation 4 units down, a reflection across the $$y$$-axis, and a translation 6 units up, what are the coordinates of the image?