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 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 a 270 degrees counterclockwise rotation a translation a translation a reflection over the line y=x

Answer 1

A 90-degree clockwise rotation about the origin can be represented by the transformation mapping $(x,y)\to (y,-x)$.

To see how this rotation is equivalent to other transformations, we can compare it to the provided options:

1. Dilation with a scale factor of $\frac{1}{4}$: This scales the distance from the origin but does not change the angle. Not equivalent.

2. Dilation with a scale factor of $\frac{1}{2}$: Similar to option 1, this just scales distances and does not change the angle. Not equivalent.

3. 270 degrees counterclockwise rotation: A 270-degree counterclockwise rotation about the origin corresponds to the transformation mapping $(x,y)\to (-y,x)$, which is the same as the 90-degree clockwise rotation, as they result in the same final positions for the points. This is equivalent.

4. Translation: Translations move points without altering their orientation, distance, or angle. Thus, not equivalent.

5. Reflection over the line $y=x$: This transforms points as follows: $(x,y)\to (y,x)$. It does not result in a 90-degree clockwise rotation and thus is not equivalent.

Among the options given, the correct response that is equivalent to a 90-degree clockwise rotation about the origin is:

A 270 degrees counterclockwise rotation.