Question

1. scale factor = ______

2 in
original
5 in

Explanation:

Step1: Recall scale factor formula

The scale factor is the ratio of the length of the new figure to the length of the original figure. So, if the original length is \( l_{original} \) and the new length is \( l_{new} \), the scale factor \( k=\frac{l_{new}}{l_{original}} \).

Step2: Identify the lengths

From the diagram, the original square has a side length of \( 2 \) inches, and the new square has a side length of \( 5 \) inches.

Step3: Calculate the scale factor

Substitute the values into the formula: \( k = \frac{5}{2}=2.5 \) or \( \frac{5}{2} \) (as a fraction).

Answer:

\( \frac{5}{2} \) (or \( 2.5 \))