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 . . .

1. Scale factor 5?
2. Scale factor 3.7?
3. Scale factor $$\frac 1 5$$?
4. Scale factor $$s$$?

Problem 2

Here are points $$A$$ and $$B$$. Plot the points for each dilation described.

1. $$C$$ is the image of $$B$$ using $$A$$ as the center of dilation and a scale factor of 2.
2. $$D$$ is the image of $$A$$ using $$B$$ as the center of dilation and a scale factor of 2.
3. $$E$$ is the image of $$B$$ using $$A$$ as the center of dilation and a scale factor of $$\frac 1 2$$.
4. $$F$$ 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 $$DEF$$.

1. Triangle $$ABC$$ is a scaled copy of triangle $$DEF$$ with what scale factor?
2. Triangle $$DEF$$ is a scaled copy of triangle $$ABC$$ with what scale factor?
(From Unit 2, Lesson 1.)

Problem 5

The diagram shows two intersecting lines.

Find the missing angle measures.

(From Unit 1, Lesson 14.)

Problem 6

1. Show that the two triangles are congruent.
2. Find the side lengths of $$DEF$$ and the angle measures of $$ABC$$.
(From Unit 1, Lesson 12.)