To determine the image of the point $(-2, -7)$ after a 90-degree counterclockwise rotation about the origin, we can apply the following transformation rule:

$(x, y) \rightarrow (-y, x)$

Here’s the process:

1. The original point is $(-2, -7)$.
2. After applying the rule:
   • $x = -2$, $y = -7$
   • New coordinates: $(-(-7), -2)$ = $(7, -2)$

Thus, the image of the point $(-2, -7)$ after a 90-degree counterclockwise rotation about the origin is (7, -2).

Would you like more details or have any questions?

Here are 5 related questions:

1. What would be the image of $(3, 5)$ after a 90-degree counterclockwise rotation?
2. How do you rotate a point 180 degrees about the origin?
3. What is the rule for a 90-degree clockwise rotation about the origin?
4. How do you find the new coordinates of a point after a 270-degree counterclockwise rotation?
5. What happens when you reflect a point across the x-axis?

Tip: For a 90-degree counterclockwise rotation, you simply switch the coordinates and change the sign of the original y-coordinate.