Final answer:
The image of the point (-6, -8) after a rotation of 90 degrees counterclockwise about the origin is (8, -6).
Step-by-step explanation:
When rotating a point (x, y) counterclockwise by 90 degrees about the origin, the new coordinates are obtained by switching the x and y coordinates and changing the sign of the new x-coordinate. Therefore, for the point (-6, -8), the x-coordinate becomes -8, and the y-coordinate becomes -(-6) = 6, giving us the point (8, 6). This rotation of 90 degrees counterclockwise about the origin swaps the x and y coordinates and negates the new x-coordinate, resulting in (8, -6) as the final image point.
To calculate the rotation, swapping the coordinates (-6, -8) to (-8, 6) represents a 90-degree counterclockwise rotation. However, as the rotation is about the origin, the new x-coordinate needs to be negated, giving the final image point as (8, -6). This transformation is consistent with the rules of rotating points about the origin on a Cartesian plane.