What is the image of the point $(-5,6)$ after a rotation of $90^{\circ}$ counferclockwise about the origin?
Answer Attempt 1 out of 2

Step 1 ：Given the point (-5, 6), we are asked to rotate it 90 degrees counterclockwise about the origin.

Step 2 ：When we rotate a point 90 degrees counterclockwise, the coordinates switch places, and the signs are adjusted based on whether or not an axis was crossed.

Step 3 ：In this case, rotating point (-5, 6) 90 degrees counterclockwise will bring it across the x-axis into Quadrant II, which means the x will be negative and the y will be positive.

Step 4 ：The original point was at (-5, 6) so the final image will be at (-6, 5).

Step 5 ：Alternatively, we could solve this problem by seeing that the slope of the segment from the origin to (-5, 6) is \(-\frac{6}{5}\).

Step 6 ：If the point is moving to a location that is a 90 degree rotation about the origin, it will move to a point on the segment perpendicular to the one that currently connects it to the origin.

Step 7 ：This will be the segment that has a slope of \(\frac{5}{6}\) or \(-\frac{5}{-6}\) from the origin which puts us at (-6, 5) or (6, -5).

Step 8 ：The point \(\boxed{(-6, 5)}\) is in the counterclockwise direction we need.