Question

a quadrilateral with sides measuring 12, 15, 9, 6 dilated to a quadrilateral with sides measuring 8, 10, 6, 4. is the scale factor

Explanation:

Step1: Recall dilation factor formula

The dilation factor $k$ is found by dividing the length of a side of the dilated figure by the length of the corresponding side of the original figure.

Step2: Choose a side - pair

Let's take the first side of each quadrilateral. The original side length $a_1 = 12$ and the dilated side length $a_2=8$.

Step3: Calculate the dilation factor

$k=\frac{a_2}{a_1}=\frac{8}{12}=\frac{2}{3}$
We can check with other sides: for the second side, $\frac{10}{15}=\frac{2}{3}$, for the third side $\frac{6}{9}=\frac{2}{3}$, and for the fourth side $\frac{4}{6}=\frac{2}{3}$.

Answer:

$\frac{2}{3}$