Question

4) Here is a polygon on a grid. (From Unit 1 Lesson 3) a. Draw a scaled copy of the polygon using a scale factor 3. Label the copy A. b. Draw a scaled copy of the polygon with a scale factor Label it B. C. Is Polygon A a scaled copy of Polygon B? d. What is the scale factor that takes B to A? Explain or show your reasoning.

Answer 1

c. Yes

d. scale factor = 6

Step-by-step explanation:

To draw a scale copy of the polygon, with a scale factor of 3, we will draw each side of the polygon with a length that is 3 times the original length. So if the figure has a side of 2 squares, the scaled figure will have the same side with 6 squares because:

2 x 3 = 6

In the same way, to draw the scaled polygon with a scale factor of 1/2, we will draw each side with a length that is half the original length. So, if the figure has a side of 2 squares, the scale figure will have a side of 1 square because:

2 x 1/2 = 1

Therefore, the scaled figures are:

Now, we can see that Polygon A is a scaled copy of polygon B. To know the scale factor that takes B to A, let's analyze one side of the figure.

So, the vertical side has 1 square on polygon B and it has 6 squares on polygon A.

Since 6/1 = 6, the scale factor that takes B to A is 6.

Therefore, the answers for parts c and d are:

c. Yes

d. scale factor = 6