Dilations

Dilations

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

Set up the proportions to determine if they are similar

 $\frac{15}{10}=\frac{9}{6}=\frac{12}{8}$  

Do these simplify to the same ratio?

Similar Figures

Set up the proportions to determine if they are similar

 $\frac{15}{10}=\frac{9}{6}=\frac{12}{8}$  

Do these simplify to the same ratio?
 $\frac{3}{2}=\frac{3}{2}=\frac{3}{2}\ \ YES!$  

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

 $\frac{24}{20}=\frac{18}{15}=\frac{12}{10}$   $\frac{6}{5}=\frac{6}{5}=\frac{6}{5}$  

Fill in the Blank

Find x using the proportional relationships of similar figures.

Set up a Proportion and Solve Like an Equation

 $\frac{25}{10}=\frac{x}{6}$  -->  $\frac{25\cdot6}{10}=x$  
 $\frac{x}{25}=\frac{6}{10}$  -->  $x=\frac{6\cdot25}{10}$  
Make sure you look at CORRESPONDING sides

To do a Dilation on the Coordinate Plane

Multiply by the scale factor!

Dilate the triangle by 3.

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

To do a Dilation on the Coordinate Plane

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

Multiply by the scale factor

  $\frac{1}{2\ }or\ 0.5$  

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

Same Starting Point, Different Factor

Multiply by the scale factor

  $\frac{1}{2\ }or\ 0.5$  

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

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

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