How is a 90-degree rotation executed?

A 90-degree rotation refers to turning a point in the coordinate plane around the origin. When executing a 90-degree rotation counterclockwise, the transformation can be visualized as moving each point to its new position by following specific rules for the coordinates.

For a point given by coordinates ((x, y)), a 90-degree counterclockwise rotation will result in the new coordinates ((-y, x)). This indicates that the x-coordinate becomes the negative y-coordinate, and the y-coordinate becomes the original x-coordinate. Therefore, graphing the coordinate and then applying the transformation results in the correct new position for that point.

Executing a 90-degree clockwise rotation would instead yield the coordinates ((y, -x)), which is why that approach isn't suitable in this case. The other options—adding the first integer to the x-coordinate or merely changing the sign of the y-coordinate—do not accurately reflect how coordinates are transformed under a 90-degree rotation. Thus, graphing the coordinate and rotating 90 degrees counterclockwise correctly captures the essence of this transformation.