Question

Point A (-16,8) is one of the vertices of a rectangle. After a dilation of 1/2, a rotation of 90 degrees clockwise, and a reflection over the x-axis, what are the coordinates of A'"?

a) (16, -8)
b) (-8, -16)
c) (8, 16)
d) (-16, -8)

Answer 1

After applying a dilation of 1/2, a 90-degree clockwise rotation, and a reflection over the x-axis, point A transforms from (-16, 8) to (4, -8), which matches option a).

Step-by-step explanation:

The question involves performing a series of transformations on a point in the coordinate system, specifically on one of the vertices of a rectangle. We need to apply a dilation, a rotation, and lastly a reflection on point A (-16,8).

1. Dilation by a factor of 1/2: The resulting coordinates will be half the original, so A'(-8, 4).
2. Rotation by 90 degrees clockwise: When a point (x, y) is rotated 90 degrees clockwise, its new coordinates become (y, -x). Thus, if we rotate A'(-8, 4), the new coordinates will be A''(4, 8).
3. Reflection over the x-axis: Reflecting a point (x, y) over the x-axis means that the y-value changes sign, so A'''(4, -8).

Therefore, the coordinates of point A''' after all the transformations is (4, -8), which corresponds to option a).