Question

(MC 02.03) If parallelogram ABCD was reflected over the y-axis, reflected over the x-axis, and rotated 180°, where would point A' lie? Parallelogram formed by ordered pairs A at negative 4, 1, B at negative 3, 2, C at 0, 2, D at negative 1, 1.

Answer 1

A' would lie on point A (-4 , 1)

Step-by-step explanation:

Let us revise some transformations

1. If point (x , y) reflected across the x-axis , then its image is (x , -y)

2. If point (x , y) reflected across the y-axis , then its image is (-x , y)

3. If point (x , y) rotated about the origin by angle 180°, then its image

    is (-x , -y)

Parallelogram ABCD was reflected over the y-axis, reflected over the

x-axis, and rotated 180°

We need to know where would point A' lie

∵ The coordinates of point A are (-4 , 1)

∵ The parallelogram is reflected over x-axis

∴ The sign of y-coordinate of point A changed to opposite

∴ The image of point A is (-4 , -1)

∵ The parallelogram then reflected over the y-axis

∴ The sign of x-coordinate of point (-4 , -1) changed to opposite

∴ The image of point (-4 , -1) is (4 , -1)

∵ The parallelogram then rotated 180°

∴ The signs of the x-coordinate and the y-coordinate of point (4 , -1)

   changed to opposite

∴ The image (4 , -1) is (-4 , 1)

∴ A' is (-4 , 1)

∵ Point A is (-4 , 1)

∴ A' would lie on point A

A' would lie on point A (-4 , 1)

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