Question

a city planner is designing a zoomed - in map of a triangular plaza. she starts with triangle abc, with vertices at (-4,2), (6,-2) and (2,4). she creates a dilation centered at the origin with a scale factor of 1.5 to produce triangle abc.
what is the ratio of the side lengths in triangle abc compared to triangle abc?
show your work here:

Explanation:

Step1: Recall the property of similar triangles

When a figure is dilated (scaled) from the origin, the ratio of the side lengths of the new figure (image) to the original figure is equal to the scale factor.

Step2: Identify the scale factor

The problem states that Triangle \(A'B'C'\) is obtained by dilating Triangle \(ABC\) with a scale factor of \(1.5\).

Answer:

The ratio of the side lengths in Triangle \(A'B'C'\) compared to Triangle \(ABC\) is \(1.5\) (or \(\frac{3}{2}\)).