Question

ΔABC has vertices A(-4,6), B (-6, -4), and C (2,-2)

The following transformation defines Δ A'''B'''C''':
ΔA'''B'''C'''=R--------------Rest in image, multiple choice.

Answer 1

A'''(0, -6), B'''(-1, -1), C'''(3, -2)

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'''