6. Describe Dilations
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Find the coordinates of the image of a dilation by multiplying the coordinates of the preimage by the scale factor.
Coordinates of preimage: D(0,0), E(2,0), F(0,2)
Multiply each coordinate by: 2
Coordinates of image: D'(0,0), E'(4,0), F'(0,4)
Graph:
We want to draw the image of △ DEF after a dilation with center at (0,0) and scale factor of 2. We also need to fill in the missing gaps. Let's do it!
First, we need to find the coordinates of triangle DEF. Keep in mind that a point is always written as an ordered pair. In the pair, the first number is the x-coordinate and the second is the y-coordinate. Let's add them onto the graph.
We can fill in the first six blanks.
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Find the coordinates of each point in the original figure. |
Now, when the center of dilation is the origin, each coordinate of the preimage is multiplied by the scale factor r. This gives us the coordinates of the image. ccc Preimage & & Image [0.5em] (x,y)& ⇒ & ( rx, ry) In our case, the scale factor is 2. We can complete the next step.
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Multiply each coordinate by 2. |
Now, let's find the coordinates of the vertices of DEF after a dilation with a scale factor r= 2.
| Dilation With Scale Factor r=2 | ||
|---|---|---|
| Preimage | Multiply by r | Image |
| D(0,0) | ( 2(0), 2(0)) | D'(0,0) |
| E(2,0) | ( 2(2), 2(0)) | E'(4,0) |
| F(0,2) | ( 2(0), 2(2)) | F'(0,4) |
We have found the coordinates of the points in the image, the triangle D'E'F'. Let's fill in the blanks.
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Find coordinates of each point in the image: D'( , ), E'(4, ), F'( ,4) |
We can now plot the obtained points. Then we will connect them with segments to draw the image.
