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
70	10
91	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 proportion formula

Let the constant of proportionality be $k$. If $y$ is the length in the scaled - copy and $x$ is the length in the original figure, then $y = kx$, so $k=\frac{y}{x}$.

Step2: Choose a row to calculate

We can choose the first row where $x = 56$ (original figure) and $y = 8$ (scaled copy). Then $k=\frac{8}{56}$.

Step3: Simplify the fraction

$\frac{8}{56}=\frac{8\div8}{56\div8}=\frac{1}{7}$. We can check with other rows. For the second row, $x = 70$ and $y = 10$, and $\frac{10}{70}=\frac{10\div10}{70\div10}=\frac{1}{7}$. For the third row, $x = 91$ and $y = 13$, and $\frac{13}{91}=\frac{13\div13}{91\div13}=\frac{1}{7}$.

Answer:

$\frac{1}{7}$