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 (−2, 4) and the image of d' is at (−1, 2). which transformation can be used to show that abcde and its image are congruent?

a. rotate abcde 90° counterclockwise.

step-by-step explanation:

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

(x,y)→ (-y,x)

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.

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