Answer:
A'''(0, -6), B'''(-1, -1), C'''(3, -2)
Step-by-step explanation:
The first transformation is dilation by a factor of 1/2, so each coordinate is multiplied by 1/2.
A' = (1/2)A = (-4, 6)/2 = (-2, 3)
The next transformation is translation, which adds (2, 3) to the coordinates.
A'' = (-2, 3) + (2, 3) = (0, 6)
The final transformation reflects across the x-axis, which negates the y-coordinate.
A''' = (0, -1·6) = (0, -6) . . . . . matches the 3rd choice for A'''
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Taken together, the transformations map (x, y) as follows:
(x, y) ⇒ (x/2 +2, -(y/2 +3))
Then
B''' = (-6/2 +2, -(-4/2 +3)) = (-1, -1) . . . matches 1st choice for B'''
C''' = (2/2 +2, -(-2/2 +3)) = (3, -2) . . . matches 3rd choice for C'''
