Eighth Grade Unit 1

Transformations

Warm Up

Homework Check

3 1/3

Dilations on the Coordinate Plane

Take one point on the pre-image and compare the ordered pair with its image point to see what the pre-image was multiplied by.

The coordinates were multiplied by 1/8: The scale factor is 1/8. We write the rule (1/8x, 1/8y)

Is this an enlargement or reduction?

Scale factor = 2

Pre-image

Image

Find the scale factor of the above dilation, determine if the pre-image was enlarged or reduced, and write the rule of dilation.

(2x, 2y)Enlarged

. Plot the image.What are the coordinates of the image?Is this an enlargement or reduction?What is the rule?

To dilate by a scale factor means to multiply the coordinates by the scale factor.

. Plot the image.

Is this an enlargement or reduction?

A

BC

DA’D’

C’ B’

What are the coordinates of the image?Is this an enlargement or reduction?What is the rule?

A’(4,-4)B’(6,4)C’(-6,4)D’(-4,-4)

Enlargement

(2x, 2y)

To dilate by a scale factor means to multiply the coordinates by the scale factor.

. Plot the image.

Is this an enlargement or reduction?What is the rule?

Plot: A(8,6) B(-4,4) C(6,-4)

Dilate by a scale factor of ½. Plot the image.What are the coordinates of the image?

To dilate by a scale factor means to multiply the coordinates by the scale factor.

Dilate by a scale factor of ½. Plot the image.What are the coordinates of the image?Is this an enlargement or reduction?What is the rule?

To dilate by a scale factor means to multiply the coordinates by the scale factor.

A

B

C

C’

B’

Plot: A(8,6) B(-4,4) C(6,-4)

A’

A’(4,3)B’(-2,2)C’(3,-2)

Reduction(½ x, ½ y)

You Try…

1. 2.

3.

A vertex of a rectangle is at (15, 12) and is dilated to (5, 4). What are the new coordinates of the second vertex of the same rectangle located at (9, 6) under the same dilation?

(3,2)

Changing Shapes

Suppose you are designing a logo for a club at your school. You draw a non-rectangular shape in a coordinate plane so that portions of the shape are in each of the four quadrants. Explain what would happen to your shape if you transformed it using the given rule with the center of dilation at the origin. Rule: (4x, 4y)

It would be four times larger.

ClosingTell which of the following rules will

produce similar figures.

a. (0.25x, 0.25y) b. (2x, y) c. (3x, 3y + 5)

d. (x + 5, y - 5)

Similar figures…the pre-image was reduced by 25%.

Not similar figures… the x and y coordinates have to be dilated by the same scale factor.

Not similar figures…the x and y coordinates have to be dilated by the same scale factor and if you translate the y coordinate, you also have to translate the x coordinate.

Not similar figures…the x and y coordinates have to be translated in the same direction.