Question

a four - sided figure is resized to create a scaled copy. the lengths of its four sides change as in the table below.

original figure	scaled copy
66	11
78	13

find the constant of proportionality from the original figure to the scaled copy. express your answer as a fraction in reduced terms.

Explanation:

Step1: Recall proportionality formula

The constant of proportionality \( k \) from original (\( x \)) to scaled (\( y \)) is \( k=\frac{y}{x} \).

Step2: Calculate for first pair

For \( x = 18 \), \( y = 3 \), \( k=\frac{3}{18}=\frac{1}{6} \).

Step3: Verify with second pair

For \( x = 66 \), \( y = 11 \), \( k=\frac{11}{66}=\frac{1}{6} \).

Step4: Verify with third pair

For \( x = 78 \), \( y = 13 \), \( k=\frac{13}{78}=\frac{1}{6} \).

Answer:

\(\frac{1}{6}\)