Question

1. is △xyz a scale drawing of △rst? explain how you know.

Explanation:

Step1: Convert mixed - numbers to improper fractions

$RS = 3\frac{1}{2}=\frac{3\times2 + 1}{2}=\frac{7}{2}$, $ST=5\frac{1}{10}=\frac{5\times10 + 1}{10}=\frac{51}{10}$, $RT = 6\frac{1}{4}=\frac{6\times4+1}{4}=\frac{25}{4}$, $XY = 5\frac{1}{4}=\frac{5\times4 + 1}{4}=\frac{21}{4}$, $YZ=7\frac{13}{20}=\frac{7\times20+13}{20}=\frac{153}{20}$, $XZ = 9\frac{3}{8}=\frac{9\times8 + 3}{8}=\frac{75}{8}$

Step2: Check the ratios of corresponding sides

$\frac{XY}{RS}=\frac{\frac{21}{4}}{\frac{7}{2}}=\frac{21}{4}\times\frac{2}{7}=\frac{3}{2}$
$\frac{YZ}{ST}=\frac{\frac{153}{20}}{\frac{51}{10}}=\frac{153}{20}\times\frac{10}{51}=\frac{3}{2}$
$\frac{XZ}{RT}=\frac{\frac{75}{8}}{\frac{25}{4}}=\frac{75}{8}\times\frac{4}{25}=\frac{3}{2}$

Since the ratios of the corresponding sides of $\triangle XYZ$ and $\triangle RST$ are equal ($\frac{XY}{RS}=\frac{YZ}{ST}=\frac{XZ}{RT}=\frac{3}{2}$), $\triangle XYZ$ is a scale - drawing of $\triangle RST$.

Answer:

Yes, $\triangle XYZ$ is a scale drawing of $\triangle RST$ because the ratios of the corresponding sides are equal.