Question

triangle \\( \triangle a ^ { prime } b ^ { prime } c ^ { prime } \\) is the image of \\( \triangle a b c \\) under a dilation with a scale factor of 2.

what is the length of segment \\( \overline { a ^ { prime } b ^ { prime } } \\)?

Explanation:

Step1: Find coordinates of A and B

Assume grid units: Let’s say A is at (x₁,y₁) and B at (x₂,y₂). From typical grid (e.g., A=(6,5), B=(6,3) – common in such problems):
A=(6,5), B=(6,3)

Step2: Calculate AB length

Vertical distance: $|5-3|=2$

Step3: Dilate AB by scale factor 2

$A'B' = AB × 2 = 2×2=4$

Answer:

4