Question

Polygon 2 is a dilation of Polygon 1, with center of dilation at (0,0). What is the scale factor?5Polygon 1321Polygon 2784-21-55-1028-4-8 -7 -6-3-1-2-3-4

Answer 1

Given: Polygon 2 is a dilation of Polygon 1

To find the scale factor, we will follow the steps below:

Step 1: Write out the coordinates of Polygon 1

Going clockwise, the coordinates are:

(6,4), (6,-4), (0,-4), (-6,2), (-2,4)

Step 2: Write out the coordinates of Polygon 2 in the same order:

The coordinates are:

(3,2), (3,-2), (0,-2), (-3, 1), (-1, 2)

Step 3:

Compare corresponding sides

Note: Since polygon 2 is a dilation of polygon 1, Polygon 2 is the image, and polygon 1 the object.

Therefore, the scale factor will be

$\text{scale factor=}\frac{\text{ coordinates of polygon 2}}{correspond\text{ing coordinates of polygon 1}}$

$\text{scale factor=}\frac{(3,2)}{(6,4)}=\frac{1}{2}$$Therefore,thescalefactor=\frac{1}{2}$