Ohio Assessments for Educators (OAE) Mathematics Practice Exam 2025 - Free Practice Questions and Study Guide

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What effect does a 90-degree clockwise rotation have in matrix terms?

Transformations remain unchanged

Coordinates are negated and interchanged

A 90-degree clockwise rotation in the context of matrix transformations involves interchanging the coordinates and negating the new x-coordinate. Mathematically, if you have a point represented by coordinates (x, y), after applying a 90-degree clockwise rotation, the new coordinates will be (y, -x).

In terms of a transformation matrix, this is represented by multiplying the original coordinate vector by the rotation matrix for 90 degrees clockwise, which is:

\[

\begin{bmatrix}

0 & 1 \\

-1 & 0

\end{bmatrix}

\]

When you multiply this matrix by the vector representing the original coordinates, you get the new coordinates as described. This shows that the transformation effectively interchanges the x and y values while negating the new x-coordinate (originally y).

This is why the correct answer indicates that coordinates are negated and interchanged to reflect the nature of a 90-degree clockwise rotation in matrix terms.

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All values become zero

Matrix values are doubled

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