If line CD is 9 inches long and is dilated by a scale factor of 1/3, how long is C'D'?

Work with a partner. Use dynamic geometry software to draw any triangle and label

it △ABC.

a. Dilate △ABC using a scale factor of 2 and a center of dilation at the origin to form

△A′B′C′. Compare the coordinates, side lengths, and angle measures of △ABC

and △A′B′C′.

D

A

B

C

A′

B′

C′

0

3

2

1

4

5

6

01 2 3 4 5 6 7 8

Sample

Points

A(2, 1)

B(1, 3)

C(3, 2)

Segments

AB = 2.24

BC = 2.24

AC = 1.41

Angles

m∠A = 71.57°

m∠B = 36.87°

m∠C = 71.57°

b. Repeat part (a) using a scale factor of 1

—2

.

c. What do the results of parts (a) and (b) suggest about the coordinates, side lengths,

and angle measures of the image of △ABC after a dilation with a scale factor of k?

Dilating Lines in a Coordinate Plane

Work with a partner. Use dynamic geometry software to draw ⃖

AB $$⃗ that passes

through the origin and ⃖

AC $$⃗ that does not pass through the origin.

a. Dilate ⃖

AB $$⃗ using a scale factor

of 3 and a center of dilation at

the origin. Describe the image.

b. Dilate ⃖

AC $$⃗ using a scale factor

of 3 and a center of dilation at

the origin. Describe the image.

c. Repeat parts (a) and (b) using a

scale factor of 1

—4

.

d. What do you notice about

dilations of lines passing

through the center of dilation

and dilations of lines not passing

through the center of dilation?

Communicate Your Answer ommunicate Your Answer

3. What does it mean to dilate a f gure?

4. Repeat Exploration 1 using a center of dilation at a point other than the origin.

Essential Question ssential Question What does it mean to dilate a f gure?

A

B C

1

Step-by-step explanation:

5.6%

step-by-step explanation:

24

step-by-step explanation: