Question

rectangle z is a scaled copy of rectangle y. what scale factor takes rectangle y to rectangle z?

Explanation:

Step1: Convert mixed numbers to improper fractions

$9\frac{1}{2}=\frac{9\times2 + 1}{2}=\frac{19}{2}$, $5\frac{1}{2}=\frac{5\times2+1}{2}=\frac{11}{2}$, $4\frac{3}{4}=\frac{4\times4 + 3}{4}=\frac{19}{4}$, $2\frac{3}{4}=\frac{2\times4+3}{4}=\frac{11}{4}$

Step2: Calculate the scale factor using the ratio of corresponding sides

We can use either the ratio of the lengths or the widths. Let's use the widths.
The scale factor $k=\frac{\text{width of }Z}{\text{width of }Y}$.
$k=\frac{\frac{11}{4}}{\frac{11}{2}}=\frac{11}{4}\times\frac{2}{11}$

Step3: Simplify the fraction

$\frac{11}{4}\times\frac{2}{11}=\frac{11\times2}{4\times11}=\frac{1}{2}$

Answer:

$\frac{1}{2}$