To determine the scale factor used to create polygon D′ from polygon D, you can use the lengths of corresponding sides of the two polygons.
For the top/bottom sides:
- Length of side in polygon D = 8
- Length of corresponding side in polygon D′ = 3.2
The scale factor is calculated as: \[ \text{Scale factor} = \frac{\text{Length of D′}}{\text{Length of D}} = \frac{3.2}{8} = 0.4 \]
Now, let's check the left/right sides to ensure consistency:
- Length of side in polygon D = 9.5
- Length of corresponding side in polygon D′ = 3.8
Calculating the scale factor for the left/right sides: \[ \text{Scale factor} = \frac{3.8}{9.5} \] To simplify this, we can divide both numbers by their greatest common divisor: \[ \frac{3.8}{9.5} = \frac{3.8 \div 3.8}{9.5 \div 3.8} = \frac{1}{2.5} = 0.4 \]
Since both corresponding sides yield the same scale factor of 0.4, we can confirm that the scale factor used to create polygon D′ from polygon D is:
Scale factor of 0.4.