Question

Point D'' (-4,-2) is a vertex of a quadrilateral A'' B'' C'' D''. The original image was rotated 270 degress counterclockwise around the origin and then reflected over the x-axis.

Part A: What are the coordinates of the original image's point D before the composition of transformations?

A. (-4,-2)
B. (-2,-4)
C. (-2,4)
D. (2,-4)

Part B: The original image is quadrilateral ABCD. Point C is on the same y-axis of point D, but five units to the right of point D. If quadrilateral A'' B'' C'' D'' is transformed following the rule (x,y)---> (x-4, y+2), what are the coordinates of point C''?
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Answer 1

steps below

Explanation:

part A: D'' (-4 , -2) (reverse) reflection over x axis -> (-4 , 2)

(-4 , 2) rotated 270 degrees clockwise: -> D (-2 , -4)

Part B: C (-2+5 , -4) = (3 , -4)

C" (3-4 , -4+2) = (-1 , -2)