Question

If trapezoid ABCD was reflected over the y-axis, reflected over the x-axis, and rotated 180°, where would point A' lie?

Answer 1

Answer: coordinates x = 1, y = 1.

Explanation:

You can deduce the answer analytically by using these mathematical rules:

1. First transformation. Reflection over the y-axis means that the image will keep the same y-coordinate and negate the x-coordinate (the image will end in the left quadrant at the same height):

• rule (x,y) → (- x, y)

          A(1,1) → A'(-1,1)

          B(2,2) → B'(-2,2)

          C(4,2) → C'(-4,2)

          D(5,1) → D'(-5,1)

2. Second transformation. The reflection over the x-axis tansforms the image by keeping the same x-coordinate and negating the y-coordinate, the image will end in the fhird quadrant right below the previous image:

• rule (x,y) → (x, - y)

          A'(-1,1) → A''(-1,-1)

          B'(-2,2) → B''(-2,-2)

          C'(-4,2) → C''(-4,-2)

          D'(-5,1) → D''(-5,-1)

3. Third transformation. The rotation 180° (either counterclockwise or clockwise) negates both coordinates x and y:

• rule (x,y) → (- x, - y)

          A''(-1,-1) → A'''(1,1) ← this is the answer

          B''(-2,-2) → B'''(2,2)

          C''(-4,-2) → C'''(4,2)

          D''(-5,-1) → D'''(5,1)

As you see the final images of every point correspond to same original point.

Answer 2

the answer is 1, 1 because it returns back to its first position