Question

triangle △abc is the image of △abc under a dilation with a scale factor of 2.
what is the length of segment ac?

Explanation:

Step1: Determine length of \( A'C' \)

Assume each grid square has side length 1. Count vertical grids between \( A' \) and \( C' \). Suppose \( A'C' \) spans \( n \) grids (e.g., if \( A' \) is at (x1,y1) and \( C' \) at (x1,y2), vertical distance is \( |y1 - y2| \)). Let's say \( A'C' = 8 \) (from grid count, vertical line).

Step2: Use scale factor for \( AC \)

Scale factor is 2, so \( \text{Length of } AC = \frac{\text{Length of } A'C'}{\text{Scale Factor}} \). Substitute \( A'C' = 8 \), scale factor = 2: \( AC = \frac{8}{2} = 4 \). (Note: If \( A'C' \) length is different, adjust. Example: if \( A'C' \) is 6 grids, \( AC = 3 \). But from typical grid, vertical \( A'C' \) might be 8, so \( AC = 4 \).)

Answer:

4 (assuming \( A'C' \) length is 8; adjust if grid count differs, but standard scale factor inverse gives \( AC = \frac{A'C'}{2} \))