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Trapezoid GHIJ is located in the coordinate plane at points G ( 0 , 0 ) , H ( − 1 , 2 ) , I ( 3 , 2 ) , and J ( 2 , 0 ) . Three transformation scenarios are described. 1. Reflect GHIJ in the x-axis and then reflect that image in the y-axis. 2. Rotate GHIJ 90º counterclockwise about the origin and then translate that image 2 units up. 3. Dilate GHIJ by a scale factor of 1 2 centered about the origin and then translate that image 2 units to the left. Which transformation(s) produce an image that is congruent to the given figure?

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abidemiokin

The transformation that produces an image that is congruent to the given figure will have a coordinate at G'''(-1, 1.5), H'''(-1, 1.5), I'''(-1, -0.5)and J'''(-2, 0)

If a coordinate (x, y) is reflected over both x and y-axis, the resulting coordinate will be at (-x, -y).

1) For the trapezoid GHIJ with coordinates G(0, 0), H(− 1, 2), I(3, 2), and J(2, 0), if it reflected over both x and y-axis, the resulting image will be at G'(1, -2), H'(1, -2), I'(-3, -2) and J'(-2, 0)

2) If the resulting image is rotated 90º counterclockwise about the origin, the resulting image will have a coordinate at G''(2, 1), H''(2, 1), I''(2, -3) and J''(0, -2)(the transformation uses is (x, y)->(-y, x)). Translating this 2 units up will give G''(2, 3), H''(2, 3), I''(2, -1) and J''(0, 0)

3) Dilating by a scale factor of 1/2 means multiplying the coordinates by 0.5 to give G'''(1, 1.5), H'''(1, 1.5), I'''(1, -0.5)and J'''(0, 0). If the final transformation is  2units to the left, the coordinates of the final figure will be produced by subtracting 2 from the x-coordinates to have  G'''(-1, 1.5), H'''(-1, 1.5), I'''(-1, -0.5)and J'''(-2, 0)

The transformation that produces an image that is congruent to the given figure will have a coordinate at G'''(-1, 1.5), H'''(-1, 1.5), I'''(-1, -0.5)and J'''(-2, 0)

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