Ohio Assessments for Educators (OAE) Mathematics Practice Exam

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

1. Transformations remain unchanged

2. Coordinates are negated and interchanged

3. All values become zero

4. Matrix values are doubled

The correct answer is: 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.