Question

what scale factor takes quadrilateral j to quadrilateral k?
quadrilateral j
quadrilateral k
quadrilateral k is a scaled copy of quadrilateral j.

Explanation:

Step1: Convert mixed numbers to improper fractions

$7\frac{1}{2}=\frac{7\times2 + 1}{2}=\frac{15}{2}$，$5\frac{1}{2}=\frac{5\times2+1}{2}=\frac{11}{2}$

Step2: Find the ratio of corresponding sides

The ratio of the sides of quadrilateral \(K\) to quadrilateral \(J\) is \(\frac{6}{\frac{15}{2}}\) (using one pair of corresponding sides).

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We can check with another pair of sides: \(\frac{\frac{11}{2}}{8}=\frac{11}{2}\times\frac{1}{8}=\frac{11}{16}\) (This is wrong, we should use correct corresponding sides. Let's use \(\frac{6}{7.5}\) (since \(7\frac{1}{2} = 7.5\)) and \(\frac{5.5}{8.5}\) (wrong approach. The correct way is to use two corresponding sides. Let's use \(\frac{6}{7.5}\) and \(\frac{5.5}{8}\) is wrong. The correct is:
If we assume the side of length \(8\) in \(J\) corresponds to a side (let's re - check the problem. Quadrilateral \(K\) is a scaled copy of \(J\). Let's take the side of length \(7\frac{1}{2}\) in \(J\) and \(6\) in \(K\).

$$ \frac{6}{7.5}=\frac{6}{\frac{15}{2}}=\frac{6\times2}{15}=\frac{12}{15}=\frac{4}{5} $$

Answer:

\(\frac{4}{5}\)