Question

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

original figure	scaled copy
44	11
52	13

find the scale factor as a fraction in reduced terms.
answer attempt 1 out of 2

Explanation:

Step1: Recall scale - factor formula

The scale factor $k$ from the original figure to the scaled - copy is given by $k=\frac{\text{Length in scaled copy}}{\text{Length in original figure}}$.

Step2: Choose a pair of lengths

Let's choose the first pair of lengths: the length in the original figure is $12$ and the length in the scaled copy is $3$. Then $k = \frac{3}{12}$.

Step3: Simplify the fraction

We simplify $\frac{3}{12}$ by dividing both the numerator and the denominator by their greatest common divisor, which is $3$. So $\frac{3\div3}{12\div3}=\frac{1}{4}$.
We can check with other pairs. For the second pair, $\frac{11}{44}=\frac{11\div11}{44\div11}=\frac{1}{4}$, and for the third pair, $\frac{13}{52}=\frac{13\div13}{52\div13}=\frac{1}{4}$.

Answer:

$\frac{1}{4}$