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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 (βˆ’4, 2) and the image of D' is at (βˆ’2, 1). Which transformation can be used to show that ABCDE and its image are congruent?

A. Rotate ABCDE 90Β° counterclockwise.
B. Translate ABCDE left 4 units and down 2 units.
C. Reflect ABCDE over the y-axis.
D. Rotate ABCDE 90Β° clockwise.

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 W class=

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ANSWER

A. Rotate ABCDE 90Β° counterclockwise.

EXPLANATION

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

[tex](x,y)\to (-y,x)[/tex]

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 90Β° counterclockwise rotation about the origin.

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

The correct answer is

A. Rotate ABCDE 90Β° counterclockwise.

Answer:

A. Rotate ABCDE 90Β° counterclockwise.

Step-by-step explanation: