Final answer:
The point (-3, -2) after a 270 degrees counterclockwise rotation around the origin will have new coordinates of (2, -3). This is achieved by switching the x and y values and changing the sign of the new x-coordinate.
Step-by-step explanation:
If the point (-3, -2) is rotated about the origin counterclockwise 270 degrees, its new coordinates can be determined by understanding the effect of rotation on points in the Cartesian plane. Rotation by 270 degrees counterclockwise is equivalent to a 90 degrees clockwise rotation, which switches the coordinate's value with a sign change on the second coordinate. Hence, the x-coordinate becomes the y-coordinate and, since it's a clockwise rotation, we change the sign of the y-coordinate to obtain the new x-coordinate. Accordingly:
- Original x-coordinate: -3
- Original y-coordinate: -2
After rotation of -3, -2 counterclockwise by 270 degrees:
- New x-coordinate = - (Original y-coordinate) = -(-2) = 2
- New y-coordinate = Original x-coordinate = -3
Therefore, the new coordinates after a 270 degrees counterclockwise rotation are (2, -3), which corresponds to option C. This process is also known as applying a rotation matrix but for middle school level, the explained approach is sufficient.