# Lesson 3

Dilations with no Grid

Let’s dilate figures not on grids.

### Problem 1

Segment \(AB\) measures 3 cm. Point \(O\) is the center of dilation. How long is the image of \(AB\) after a dilation with . . .

- Scale factor 5?
- Scale factor 3.7?
- Scale factor \(\frac 1 5\)?
- Scale factor \(s\)?

### Problem 2

Here are points \(A\) and \(B\). Plot the points for each dilation described.

- \(C\) is the image of \(B\) using \(A\) as the center of dilation and a scale factor of 2.
- \(D\) is the image of \(A\) using \(B\) as the center of dilation and a scale factor of 2.
- \(E\) is the image of \(B\) using \(A\) as the center of dilation and a scale factor of \(\frac 1 2\).
- \(F\) is the image of \(A\) using \(B\) as the center of dilation and a scale factor of \(\frac 1 2\).

### Problem 3

Make a perspective drawing. Include in your work the center of dilation, the shape you dilate, and the scale factor you use.

### Problem 4

Triangle \(ABC\) is a scaled copy of triangle \(DEF\). Side \(AB\) measures 12 cm and is the longest side of \(ABC\). Side \(DE\) measures 8 cm and is the longest side of \(DEF\).

- Triangle \(ABC\) is a scaled copy of triangle \(DEF\) with what scale factor?
- Triangle \(DEF\) is a scaled copy of triangle \(ABC\) with what scale factor?

### Problem 5

The diagram shows two intersecting lines.

Find the missing angle measures.

### Problem 6

- Show that the two triangles are congruent.
- Find the side lengths of \(DEF\) and the angle measures of \(ABC\).