Lesson 5
The Size of the Scale Factor
Let’s look at the effects of different scale factors.
Problem 1
Rectangles P, Q, R, and S are scaled copies of one another. For each pair, decide if the scale factor from one to the other is greater than 1, equal to 1, or less than 1.
![Four rectangles, labeled P, Q, R and S.](https://cms-im.s3.amazonaws.com/r92sCFtwgkGK3qLKRXxxY76s?response-content-disposition=inline%3B%20filename%3D%227-7.1.A.PP.Image.22.png%22%3B%20filename%2A%3DUTF-8%27%277-7.1.A.PP.Image.22.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240630%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240630T162152Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=14943f3f25a033c9076448a88eb10c16d5d3713246fac18c00b76791054d0572)
- from P to Q
- from P to R
- from Q to S
- from Q to R
- from S to P
- from R to P
- from P to S
Problem 2
Triangle S and Triangle L are scaled copies of one another.
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What is the scale factor from S to L?
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What is the scale factor from L to S?
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Triangle M is also a scaled copy of S. The scale factor from S to M is \(\frac{3}{2}\). What is the scale factor from M to S?
![Two triangles labeled S and L on a grid. Triangle S has a horizontal base of 2 units and a height of 4 units. Triangle L has a horizontal base of 4 units and a height of 8 units.](https://cms-im.s3.amazonaws.com/QzSG8Ti4pi8B684RjAQQEcZQ?response-content-disposition=inline%3B%20filename%3D%227-7.1.A.PP.Image.31.png%22%3B%20filename%2A%3DUTF-8%27%277-7.1.A.PP.Image.31.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240630%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240630T162152Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=11fe35352ae8c879d7d5e19baf9a76b6bc76563cfe9198c2afae87ebbb04137b)
Problem 3
Are two squares with the same side lengths scaled copies of one another? Explain your reasoning.
Problem 4
Quadrilateral A has side lengths 2, 3, 5, and 6. Quadrilateral B has side lengths 4, 5, 8, and 10. Could one of the quadrilaterals be a scaled copy of the other? Explain.
Problem 5
Select all the ratios that are equivalent to the ratio \(12:3\).
\(6:1\)
\(1:4\)
\(4:1\)
\(24:6\)
\(15:6\)
\(1,\!200:300\)
\(112:13\)