Question

1. polygon y is a scaled copy of polygon x.

1. what is the value of d?

Explanation:

Step1: Find the scale factor

First, convert mixed numbers to improper fractions:
$4\frac{1}{2} = \frac{9}{2}$, $6\frac{3}{4} = \frac{27}{4}$
Scale factor $k = \frac{\text{Side of Y}}{\text{Side of X}} = \frac{\frac{27}{4}}{\frac{9}{2}} = \frac{27}{4} \times \frac{2}{9} = \frac{3}{2}$

Step2: Verify scale factor with another side

$7\frac{1}{2} = \frac{15}{2}$, $9\frac{3}{4} = \frac{39}{4}$
Check $k = \frac{\frac{39}{4}}{\frac{15}{2}} = \frac{39}{4} \times \frac{2}{15} = \frac{3}{2}$ (matches)

Step3: Calculate $z$ using scale factor

Since the corresponding side in X is 2, $z = 2 \times \frac{3}{2}$

Answer:

$3$