Polygon abcde is the first in a pattern for a high school art project. the polygon is transformed so that the image of a' is at (−4, 2) and the image of d' is at (−2, 1). which transformation can be used to show that abcde and its image are congruent?
a. rotate abcde 90° counterclockwise.
b. translate abcde left 4 units and down 2 units.
c. reflect abcde over the y-axis.
d. rotate abcde 90° clockwise.

ANSWER

A. Rotate ABCDE 90° counterclockwise.

EXPLANATION

When we rotate a point through 90° counterclockwise, the mapping is

The coordinates of A are (2,4) and the coordinates of A' are (-4,2)

The coordinates of D are (1,2) and the coordinates of D' are (-2,1).

We can observe that the x and y coordinates swapped position and the first coordinate was then negated.

This is a 90° counterclockwise rotation about the origin.

Since rotation is a rigid motion the two shapes are congruent.

The correct answer is

A. Rotate ABCDE 90° counterclockwise.