Question

1. a quadrilateral with sides measuring 12, 4, 6, and 8 meters is dilated to create a quadrilateral with sides measuring 9, 3, 9/2, and 6 meters

Explanation:

Step1: Find the scale - factor

To find the scale - factor of dilation, divide the length of a side of the new quadrilateral by the length of the corresponding side of the original quadrilateral. Let's take the first pair of corresponding sides. If the original side length is 4 meters and the new side length is 9 meters, the scale - factor $k=\frac{9}{4} = 2.25$. We can check with other sides. For example, if the original side is 6 meters and the new side is $\frac{27}{2}=13.5$ meters, and $\frac{13.5}{6}=2.25$.

Step2: Find the length of the dilated side corresponding to 8 meters

Multiply the length of the original side (8 meters) by the scale - factor. Let the length of the dilated side be $x$. Then $x = 8\times k$. Since $k = 2.25$, we have $x=8\times2.25=18$ meters.

Step3: Find the length of the dilated side corresponding to 12 meters

Multiply the length of the original side (12 meters) by the scale - factor. Let the length of the dilated side be $y$. Then $y = 12\times k$. Since $k = 2.25$, we have $y=12\times2.25 = 27$ meters.

Answer:

The side lengths of the dilated quadrilateral are 18 meters and 27 meters.