Warm Up:

• Why do we use dilations to create scale drawings of figures? (Think about the properties of a scale drawing)• Please answer in full sentences.

Dilations Practice

Do you understand the properties of dilations?

1. A dilation with center O and scale factor r takes A to A’ and B to B’. Find the center O and estimate the scale factor r.

1. A dilation with center O and scale factor r takes A to A’ and B to B’. Find the center O and estimate the scale factor r.

1. A dilation with center O and scale factor r takes A to A’ and B to B’. Find the center O and estimate the scale factor r.I know that the center O will lie on line AA’ and line BB’. I will draw line AA’ and line BB’.

1. A dilation with center O and scale factor r takes A to A’ and B to B’. Find the center O and estimate the scale factor r.I know that the center O will lie on line AA’ and line BB’. I will draw line AA’ and line BB’.

1. A dilation with center O and scale factor r takes A to A’ and B to B’. Find the center O and estimate the scale factor r.The only point that lies on line AA’ and line BB’ is the point of intersection. That is my center O.

1. A dilation with center O and scale factor r takes A to A’ and B to B’. Find the center O and estimate the scale factor r.The only point that lies on line AA’ and line BB’ is the point of intersection. That is my center O.

O

1. A dilation with center O and scale factor r takes A to A’ and B to B’. Find the center O and estimate the scale factor r.To find the scale factor, I compare length OA to OA’ and OB to OB’.

O

1. A dilation with center O and scale factor r takes A to A’ and B to B’. Find the center O and estimate the scale factor r.I find that OA’ is twice the length of OA. OB’ is twice the length of OB. Therefore, my scale factor is r=2.

O

Given a center , scale factor , and points and , find the points and . Compare length with length by division; in other words, find . How does this number compare to ?

Given a center , scale factor , and points and , find the points and . Compare length with length by division; in other words, find . How does this number compare to ?

Given a center , scale factor , and points and , find the points and . Compare length with length by division; in other words, find . How does this number compare to ?

I begin by finding A’ and B’. I draw rays OA and OB. Then I dilate A and B using the scale factor r = 3.

Given a center , scale factor , and points and , find the points and . Compare length with length by division; in other words, find . How does this number compare to ?

I begin by finding A’ and B’. I draw rays OA and OB. Then I dilate A and B using the scale factor r = 3.

Given a center , scale factor , and points and , find the points and . Compare length with length by division; in other words, find . How does this number compare to ?

Now measure A’B’ and AB.

Given a center , scale factor , and points and , find the points and . Compare length with length by division; in other words, find . How does this number compare to ?

A’B’=12.6 units. AB = 4.2 units.

Given a center , scale factor , and points and , find the points and . Compare length with length by division; in other words, find . How does this number compare to ?

A’B’=12.6 units. AB = 4.2 units.So =

Given a center , scale factor , and points and , find the points and . Compare length with length by division; in other words, find . How does this number compare to ?

A’B’=12.6 units. AB = 4.2 units.So = This number, , is equal to r.

3. Given a center , scale factor , and points ,, and , find the points , , and . Compare with . What do you find?

3. Given a center , scale factor , and points ,, and , find the points , , and . Compare with . What do you find?

First, I must find A’, B’, and C’ using a dilation with scale factor r=3.

3. Given a center , scale factor , and points ,, and , find the points , , and . Compare with . What do you find?

First, I must find A’, B’, and C’ using a dilation with scale factor r=3.

3. Given a center , scale factor , and points ,, and , find the points , , and . Compare with . What do you find?

Now I compare with . I see the angle measurements are equal.

4. Describe a dilation that maps , and then use your dilation to locate , the image of .

4. Describe a dilation that maps , and then use your dilation to locate , the image of .

I know the center of dilation O will lie on the line AA’.

4. Describe a dilation that maps , and then use your dilation to locate , the image of .

I know the center of dilation O will lie on the line AA’.

4. Describe a dilation that maps , and then use your dilation to locate , the image of .

I know the center of dilation O will lie on the line AA’. I can put O on the left of A or on the right of A’.

4. Describe a dilation that maps , and then use your dilation to locate , the image of .

I know the center of dilation O will lie on the line AA’. I can put O on the left of A or on the right of A’.

O

4. Describe a dilation that maps , and then use your dilation to locate , the image of .

I measure OA and OA’ to find , my scale factor (from Exercise 2).

O

4. Describe a dilation that maps , and then use your dilation to locate , the image of .

OA=8 units. OA’=2 units. So r=.

O

4. Describe a dilation that maps , and then use your dilation to locate , the image of .

Now I dilate P with scale factor r=1/4.

OP’