warm up: why do we use dilations to create scale drawings of figures? (think about the properties of...
Post on 21-Dec-2015
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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.
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 .
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
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