Question

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

Explanation:

Step1: Convert mixed - numbers to improper fractions

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

Step2: Check the ratios of corresponding sides

Ratio of side $RS$ to side $XY$: $\frac{RS}{XY}=\frac{\frac{7}{2}}{\frac{21}{4}}=\frac{7}{2}\times\frac{4}{21}=\frac{2}{3}$
Ratio of side $ST$ to side $YZ$: $\frac{ST}{YZ}=\frac{\frac{51}{10}}{\frac{153}{20}}=\frac{51}{10}\times\frac{20}{153}=\frac{2}{3}$
Ratio of side $RT$ to side $XZ$: $\frac{RT}{XZ}=\frac{\frac{25}{4}}{\frac{75}{8}}=\frac{25}{4}\times\frac{8}{75}=\frac{2}{3}$
Since the ratios of all corresponding sides are equal.

Answer:

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