Question

Polygon D has been dilated to create polygon D′.

Polygon D with top and bottom sides labeled 8 and left and right sides labeled 9.5. Polygon D prime with top and bottom sides labeled 3.2 and left and right sides labeled 3.8.

Determine the scale factor used to create the image.

Scale factor of 0.4
Scale factor of 2.5
Scale factor of 0.2
Scale factor of 1.2

Answer 1

To determine the scale factor of the dilation from polygon D to polygon D′, we can compare the corresponding sides of the two polygons.

The top and bottom sides of polygon D are 8, and in polygon D′, the corresponding sides are 3.2.

To find the scale factor, we divide the corresponding side of polygon D′ by the corresponding side of polygon D:

\[
\text{Scale Factor} = \frac{\text{Length of Side in D'}}{\text{Length of Side in D}} = \frac{3.2}{8}
\]

Calculating the above expression:

\[
\text{Scale Factor} = \frac{3.2}{8} = 0.4
\]

Next, we can verify this using the left and right sides. The left and right sides of polygon D are 9.5, and in polygon D′, the corresponding sides are 3.8.

Calculate the scale factor using these sides as well:

\[
\text{Scale Factor} = \frac{3.8}{9.5}
\]

Now calculating:

\[
\text{Scale Factor} = \frac{3.8}{9.5} = 0.4
\]

Both comparisons give us the same scale factor.

Therefore, the scale factor used to create the image is:

**Scale factor of 0.4**