Lesson 9
Dilations
Problem 1
Here is triangle \(ABC\).
![Triangle A B C and point P on a circular grid. The coordinates of triangle A B C are A(negative 2 comma 2), B(negative 4 comma negative 1) and C(3 comma negative 1) and of point P at P(0 comma 0).](https://cms-im.s3.amazonaws.com/EuiRajwScmuwfumv9qAb3rMf?response-content-disposition=inline%3B%20filename%3D%228-8.2.A2.newPP.Image.05.png%22%3B%20filename%2A%3DUTF-8%27%278-8.2.A2.newPP.Image.05.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T004928Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=3a73c61de6651155bf0199f9bb123d6b1a5486953f0f6ca055297a3fff51a899)
- Dilate each vertex of triangle \(ABC\) using \(P\) as the center of dilation and a scale factor of 2. Draw the triangle connecting the three new points.
- Dilate each vertex of triangle \(ABC\) using \(P\) as the center of dilation and a scale factor of \(\frac 1 2\). Draw the triangle connecting the three new points.
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Measure the longest side of each of the three triangles. What do you notice?
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Measure the angles of each triangle. What do you notice?
Solution
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Problem 2
Segment \(AB\) measures 3 cm. Point \(O\) is the center of dilation. How long is the image of \(AB\) after a dilation with . . .
- Scale factor 5?
- Scale factor 3.7?
- Scale factor \(\frac 1 5\)?
- Scale factor \(s\)?
Solution
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Problem 3
Here are points \(A\) and \(B\). Plot the points for each dilation described.
![Points A and B](https://cms-im.s3.amazonaws.com/kWYCmiQXpZ9nAnADWXPXqhZc?response-content-disposition=inline%3B%20filename%3D%228-8.2.A2.Image.10.png%22%3B%20filename%2A%3DUTF-8%27%278-8.2.A2.Image.10.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T004928Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=14f7aa42db0bfc52e0c98df536ef85e77ae0186a71cd3a31f66b4435d719b7ae)
- \(C\) is the image of \(B\) using \(A\) as the center of dilation and a scale factor of 2.
- \(D\) is the image of \(A\) using \(B\) as the center of dilation and a scale factor of 2.
- \(E\) is the image of \(B\) using \(A\) as the center of dilation and a scale factor of \(\frac 1 2\).
- \(F\) is the image of \(A\) using \(B\) as the center of dilation and a scale factor of \(\frac 1 2\).
Solution
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Problem 4
Make a perspective drawing. Include in your work the center of dilation, the shape you dilate, and the scale factor you use.
Solution
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