Question

a triangle with sides measuring 6, 12, 4 dilated to a triangle with sides measuring 9, 18, 6.

Explanation:

Step1: Find the scale - factor for each side

For the first side: $\frac{9}{6}=\frac{3}{2}$; for the second side: $\frac{18}{12}=\frac{3}{2}$; for the third side: $\frac{6}{4}=\frac{3}{2}$.

Step2: Determine the scale - factor of dilation

Since the ratio of the corresponding sides of the two triangles is the same ($\frac{3}{2}$), the scale - factor of dilation is $\frac{3}{2}$.

Answer:

The scale - factor of dilation is $\frac{3}{2}$.