Question

The rotation function mapping for a 90-degree clockwise rotation about the origin is equivalent to which other transformation mapping?
A. a dilation with a scale factor of 1/4
B. A translation
C. a reflection over the line y = x
D. a 270 degrees counterclockwise rotation

Answer 1

To analyze the transformation resulting from a 90-degree clockwise rotation about the origin, we can express the mapping mathematically.

In a Cartesian coordinate system, a point \((x, y)\) after a 90-degree clockwise rotation maps to \((y, -x)\).

Now, we can evaluate the given options:

A. A dilation with a scale factor of 1/4:
- This would scale the coordinates down but not change them in orientation, so it does not match a 90-degree clockwise rotation.

B. A translation:
- A translation moves every point by the same distance in the same direction, which does not result in the rotation effect.

C. A reflection over the line \(y = x\):
- Reflecting a point \((x, y)\) over the line \(y = x\) maps it to \((y, x)\), which is not the same as a 90-degree clockwise rotation.

D. A 270 degrees counterclockwise rotation:
- A 270 degrees counterclockwise rotation is equivalent to a 90 degrees clockwise rotation. Mathematically, a 270 degrees counterclockwise rotation maps a point \((x, y)\) to \((-y, x)\), which corresponds to what is effectively described if we think of the rotation in the opposite direction as a 90 degrees clockwise rotation.

Given this analysis, the correct answer is:
**D. a 270 degrees counterclockwise rotation.**