Question

The rotation function mapping for a 90-degree clockwise rotation about the origin is equivalent to which other transformation mapping?(1 point) Responses a translation a translation a reflection over the line y=x a reflection over the line y equals x a dilation with a scale factor of 14 a dilation with a scale factor of Start Fraction 1 over 2 End Fraction a 270 degrees counterclockwise rotation

Answer 1

A 90-degree clockwise rotation about the origin can be expressed mathematically as the transformation \( (x, y) \) to \( (y, -x) \).

Looking at the options provided:

1. **A translation** - This does not relate to a rotation.
2. **A reflection over the line \( y = x \)** - This transformation takes \( (x, y) \) to \( (y, x) \), which is not the same as our rotation.
3. **A dilation with a scale factor of \( 14 \)** - This does not relate to rotations.
4. **A dilation with a scale factor of \( \frac{1}{2} \)** - This does not relate to rotations.
5. **A 270 degrees counterclockwise rotation** - A 270 degrees counterclockwise rotation is equivalent to a 90 degrees clockwise rotation.

Therefore, the correct answer is:
**A 270 degrees counterclockwise rotation.**