Question

1. a quadrilateral with sides measuring 12, 4, 6, and 8 meters is dilated to create a quadrilateral with sides measuring 9, 3, $\frac{9}{2}$, and 6 meters

Explanation:

Step1: Recall dilation ratio formula

Dilation ratio = new side length / original side length

Step2: Calculate dilation ratio for first - side

For the first side, original length is 12 meters and new length is 9 meters. Dilation ratio $r=\frac{9}{12}=\frac{3}{4}$

Step3: Check for other sides

For the second side: original length is 4 meters, new length is 3 meters. $\frac{3}{4}=\frac{3}{4}$
For the third side: original length is 6 meters, new length is $\frac{9}{2}$ meters. $\frac{\frac{9}{2}}{6}=\frac{9}{2\times6}=\frac{3}{4}$
For the fourth side: original length is 8 meters, new length is 6 meters. $\frac{6}{8}=\frac{3}{4}$

Answer:

The dilation ratio is $\frac{3}{4}$