Dilations and Scale Factors

Dilations and Scale Factors

Multiple Select

Which statements are true about Dilations?

• They are rigid transformations

• They are non-rigid transformations

• They change the size of a shape (bigger or smaller)

• They change a shape

Scale Factors

> 1 Enlargement

> 0 & < 1 Reduction

=0 Makes it a point

Negative: Reflection through Point (Center of Dilation)

Multiple Select

Similar figures have ...

• Congruent Angles

• Congruent Side Lengths

• Proportional Angles

• Proportional Side Lengths

Multiple Choice

Are these similar figures?

• Yes

• No

Similar Figures

Multiple Choice

Are the two figures similar?

• Yes

• No

Multiple Choice

Are the two figures similar?

• Yes

• No

Make sure to set up ratios with corresponding sides

Fill in the Blank

Find x using the proportional relationships of similar figures.

Set up a Proportion and Solve Like an Equation

To do a Dilation on the Coordinate Plane (when centered at the origin)

Multiply by the scale factor!

Dilate the triangle by 3.

F(2, -2), G(2, 2), H(-1, -2)

Multiply by the scale factor!

Dilate the triangle by 3.

F(2, -2), G(2, 2), H(-1, -2)

F'(6, -6), G'(6, 6), H'(-3, -6)

Same Starting Point, Different Factor

Fill in the Blank

Dilate by a factor of 5.

A(2, 3), B(1, 4), C(4, 5)

Fill in the Blank

Similar figures have _____ angles.

Fill in the Blank

Similar figures have _____ side lengths.

Multiple Choice

A figure has a point at (3, 4). When dilated by a factor of 2, the new image point is located where?

• (5, 6)

• (5, 8)

• (6, 8)

• (6, 6)

Multiple Choice

Find x.

• 18

• 14

• 12

• 11

Multiple Choice

Find x.

• 6

• 9

Dilations Not Centered at the Origin

The points will still move in a straight line toward or away from the center point!

​

​Dilations can be centered anywhere!

​Dilations can be centered anywhere!

Multiple Choice

What is the scale factor of this dilation?

• $$2$$

• $$3$$

• $$\frac{1}{3}$$

• $$\frac{1}{2}$$

Multiple Choice

What are the coordinates for the center of dilation?

• (2, 9)

• (7, 1)

• (0, 0)

• (2, -3)

Multiple Choice

What are the coordinates for the center of dilation?

• (-1, 4)

• (0, 0)

• (3, 1)

• (7, -9)

Hotspot

Segment CD is dilated from point O by a scale factor of 4. Where are C' and D' located?

(Choose TWO points, one for C and one for D.)