To find the image of the point $(8, 7)$ after a 90° counterclockwise rotation about the origin, we use the following rule for rotations:

If a point $(x, y)$ is rotated 90° counterclockwise about the origin, its new coordinates become:

$(x', y') = (-y, x)$

Step-by-Step Solution:

1. The original point is $(8, 7)$, so $x = 8$ and $y = 7$.
2. Applying the formula for 90° counterclockwise rotation: $(x', y') = (-7, 8)$

Final Answer:

The image of the point $(8, 7)$ after a 90° counterclockwise rotation about the origin is $(-7, 8)$.

Would you like a detailed explanation or any clarifications on this process? Here are some related questions you might find helpful:

1. What is the image of $(8, 7)$ after a 180° rotation?
2. How do you perform a 270° counterclockwise rotation about the origin?
3. What is the general formula for rotating any point by 90° clockwise?
4. How would the coordinates change if the point was reflected across the y-axis instead of rotated?
5. Can you explain how to rotate a point by 45° counterclockwise?

Tip: Always remember that a 90° counterclockwise rotation switches the coordinates and changes the sign of the original $y$-coordinate.