Question

Which graph shows a dilation?

On a coordinate plane, 2 quadrilaterals are shown. The larger quadrilateral has points (negative 4, 3), (0, 3), (2, 0), and (negative 2, 0). The smaller quadrilateral has points (negative 2, 2), (0, 2), (0.5, 0), and (negative 1.5, 0).
On a coordinate plane, 2 quadrilaterals are shown. The larger quadrilateral has points (negative 4, 3), (0, 3), (2, 0), and (negative 2, 0). The smaller quadrilateral has points (negative 2, 2), (0, 2), (0.5, 0), and (negative 1.5, 0).
On a coordinate plane, 2 quadrilaterals are shown. The larger quadrilateral has points (negative 5, 3), (1, 3), (4, 0), (negative 2, 0). The smaller quadrilateral has points (negative 1, 0), (negative 2, 1), (0, 1), and (1, 0).
On a coordinate plane, 2 quadrilaterals are shown. The larger quadrilateral has points (negative 5, 3), (1, 3), (4, 0), (negative 2, 0). The smaller quadrilateral has points (negative 0.5, 0), (negative 1, 2), (1, 2), (1.5, 0).

Answer 1

The third graph (large: (-5,3),(1,3),(4,0),(-2,0); small: (-1,0),(-2,1),(0,1),(1,0)) is a dilation.

Reason: the center is S = (-0.5, 0). Points pair up along lines through S and the scale factor is 1/3. For example,
- (4,0) -> (1,0): both lie on y=0 with distances from S: 4.5 and 1.5, ratio 1.5/4.5 = 1/3.
- (-5,3) -> (-2,1): both on the line through S with vector from S scaled by 1/3 ((-4.5,3) scaled gives (-1.5,1)).

All vertices match this same center and scale, so the third graph shows a dilation.