Question

side length of original triangle corresponding side length in scaled copy
9 3
12 4
the scale factor is □.

Explanation:

Step1: Recall scale - factor formula

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

Step2: Use the first pair of side - lengths

Using the first row of the table where the side length of the original triangle is $9$ and the corresponding side length in the scaled copy is $3$. Then $k = \frac{3}{9}=\frac{1}{3}$.

Step3: Verify with the second pair of side - lengths

Using the second row of the table where the side length of the original triangle is $12$ and the corresponding side length in the scaled copy is $4$. Then $k=\frac{4}{12}=\frac{1}{3}$.

Answer:

$\frac{1}{3}$