Lesson 4

Dilations on a Square Grid

Let’s dilate figures 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.

Triangle A B C, it’s image after dilation triangle A prime B prime C prime and point D.

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 \(\frac{1}{2}\).
Quadrilateral P Q R S and point O on a square grid.

Problem 3

The diagram shows three lines with some marked angle measures.

Three lines in a plane. 

Find the missing angle measures marked with question marks.

(From Unit 1, Lesson 14.)

Problem 4

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

two of the same figure on a square grid in different orientations and position

 

(From Unit 1, Lesson 4.)

Problem 5

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?

(From Unit 1, Lesson 6.)