Question

question 3
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:

Dilation changes size proportionally. Rotation turns a figure, reflection flips it. Here, scale - factor 1.5 implies size change (dilation). No turning (rotation) or flipping (reflection) signs.

Answer:

A dilation changes the size of a figure proportionally. A rotation turns a figure around a point, and a reflection flips a figure over a line. Since the transformation here has a scale factor of \(1.5\) (which changes the size of Triangle \(ABC\) to get Triangle \(A'B'C'\)) and there is no indication of turning (as in rotation) or flipping (as in reflection), it is a dilation.