Geometry Regents Practice Exam

When a point (x, y) is rotated 270 degrees counterclockwise, it results in the transformation of the coordinates to a new position. To find the correct transformation equation, it helps to visualize or recall the typical rotation transformations.

A 270-degree counterclockwise rotation can also be considered equivalent to a 90-degree clockwise rotation. Here’s how the coordinates change during the rotation:

- A 90-degree clockwise rotation transforms the point (x, y) to (y, -x).

- Therefore, when considering a 270-degree counterclockwise rotation (which is the same as moving clockwise through 90 degrees), you can deduce that the coordinates switch places and also undergo a sign change.

This can be further confirmed by reflecting on known rotation transformations:

1. A 90-degree counterclockwise rotation transforms (x, y) to (-y, x).

2. A 180-degree rotation shifts (x, y) to (-x, -y).

3. A 270-degree counterclockwise rotation results in (y, -x), which is consistent with being the transformation following the previous rotations.

Hence, the correct transformation for a rotation of 270 degrees counterclockwise yields the coordinates (y, -x