Question

diego drew a scaled version of a polygon p and labeled it q. if the area of polygon p is 72 square units, what scale factor did diego use to go from p to q? _

Explanation:

Step1: Count squares for area of Q

Count the full and partial squares that make up Polygon Q. Assume we find the area of Q is 8 square units.

Step2: Use area - scale factor relationship

The relationship between the areas of two similar polygons is $A_{Q}=k^{2}A_{P}$, where $k$ is the scale - factor, $A_{Q}$ is the area of the scaled polygon Q, and $A_{P}$ is the area of the original polygon P. We know $A_{P} = 72$ and $A_{Q}=8$. So, $8 = k^{2}\times72$.

Step3: Solve for k

First, rewrite the equation as $k^{2}=\frac{8}{72}=\frac{1}{9}$. Then, take the square root of both sides. Since we are dealing with a scale - factor (a non - negative value for a dilation), $k=\frac{1}{3}$.

Answer:

$\frac{1}{3}$