Question

what is the scale factor? * image of two triangles on a grid with a point p your answer

Explanation:

Step1: Determine lengths of corresponding sides

First, find the length of \( AB \) and \( A'B' \) using the grid. Let's assume each grid square has side length 1. The length of \( AB \) (from \( B \) to \( A \)) is 2 units (since it spans 2 grid squares horizontally). The length of \( A'B' \) (from \( B' \) to \( A' \)) is 1 unit (spans 1 grid square horizontally).

Step2: Calculate scale factor

The scale factor is the ratio of the length of a side of the image (\( A'B'C' \)) to the length of the corresponding side of the original figure (\( ABC \)). So, scale factor \( = \frac{\text{Length of } A'B'}{\text{Length of } AB} = \frac{1}{2} \). We can also check the vertical sides: length of \( AC \) (vertical) is 4 units (spans 4 grid squares), length of \( A'C' \) is 2 units. \( \frac{2}{4} = \frac{1}{2} \), confirming the scale factor.

Answer:

\(\frac{1}{2}\)