# Lesson 10

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.

### Problem 2

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

- The dilation centered at \(R\) with scale factor 2.
- The dilation centered at \(O\) with scale factor \(\frac{1}{2}\).
- The dilation centered at \(S\) with scale factor \(\frac{1}{2}\).

### Problem 3

Quadrilateral \(ABCD\) is dilated with center \((0,0)\), taking \(B\) to \(B'\). Draw \(A'B'C'D'\).

### Problem 4

Triangles \(B\) and \(C\) have been built by dilating Triangle \(A\).

- Find the center of dilation.
- Triangle \(B\) is a dilation of \(A\) with approximately what scale factor?
- Triangle \(A\) is a dilation of \(B\) with approximately what scale factor?
- Triangle \(B\) is a dilation of \(C\) with approximately what scale factor?

### Problem 5

Here is a triangle.

- Draw the dilation of triangle \(ABC\), with center \((0,0)\), and scale factor 2. Label this triangle \(A’B’C’\).
- Draw the dilation of triangle \(ABC\), with center \((0,0)\), and scale factor \(\frac{1}{2}\). Label this triangle \(A’’B’’C’’\).
- Is \(A’’B’’C’’\) a dilation of triangle \(A’B’C’\)? If yes, what are the center of dilation and the scale factor?

### Problem 6

The diagram shows three lines with some marked angle measures.

Find the missing angle measures marked with question marks.