Question

trapezoid r is a scaled copy of trapezoid q. what is the value of y?

Explanation:

Step1: Convert mixed numbers to improper fractions

• \(1\frac{3}{4}=\frac{1\times4 + 3}{4}=\frac{7}{4}\)
• \(1\frac{2}{5}=\frac{1\times5+2}{5}=\frac{7}{5}\)
• \(1\frac{1}{2}=\frac{1\times2 + 1}{2}=\frac{3}{2}\)
• \(2\frac{3}{4}=\frac{2\times4+3}{4}=\frac{11}{4}\)
• \(2\frac{1}{5}=\frac{2\times5 + 1}{5}=\frac{11}{5}\)

Step2: Find the scale factor

Since trapezoid \(R\) is a scaled - copy of trapezoid \(Q\), the scale factor \(k\) can be found by the ratio of corresponding sides. Let's use the non - parallel sides.
\(k=\frac{1\frac{2}{5}}{1\frac{3}{4}}=\frac{\frac{7}{5}}{\frac{7}{4}}=\frac{7}{5}\times\frac{4}{7}=\frac{4}{5}\)

Step3: Calculate the value of \(y\)

We know that \(y\) corresponds to \(1\frac{1}{2}\) in trapezoid \(Q\). Using the scale factor \(k = \frac{4}{5}\)
\(y=1\frac{1}{2}\times\frac{4}{5}\)
\(y=\frac{3}{2}\times\frac{4}{5}\)
\(y=\frac{3\times4}{2\times5}=\frac{12}{10}=\frac{6}{5}=1\frac{1}{5}\)

Answer:

\(1\frac{1}{5}\)