Question

how do you know this transformation is a dilation and not a rotation or reflection?
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), and creates a dilation centered at the origin with a scale factor of 1.5 to produce triangle abc.

Explanation:

A dilation changes the size of a figure. A rotation turns a figure around a point, and a reflection flips a figure over a line. Since the problem mentions a scale factor (which is characteristic of dilation - it resizes the figure) and no mention of turning (rotation) or flipping (reflection) is made, it's a dilation.

Answer:

A dilation changes the size of a figure using a scale factor. A rotation turns a figure around a point, and a reflection flips a figure over a line. Here, since there's a scale factor (1.5) mentioned (a key element of dilation) and no mention of rotation (turning) or reflection (flipping), it is a dilation.