To find the image of the point $(-7, -8)$ after a rotation of 270° counterclockwise about the origin, we can use the standard formula for rotating a point $(x, y)$ by an angle $\theta$ around the origin. The formulas for rotations are:

• A 90° counterclockwise rotation: $(x, y) \rightarrow (-y, x)$
• A 180° counterclockwise rotation: $(x, y) \rightarrow (-x, -y)$
• A 270° counterclockwise rotation: $(x, y) \rightarrow (y, -x)$

For a 270° counterclockwise rotation, we apply the formula $(x, y) \rightarrow (y, -x)$.

Given the point $(-7, -8)$:

• $x = -7$
• $y = -8$

Using the formula for a 270° counterclockwise rotation: $(x, y) \rightarrow (y, -x)$ So the new coordinates will be: $(-8, 7)$

Therefore, the image of the point $(-7, -8)$ after a 270° counterclockwise rotation about the origin is $(-8, 7)$.

Would you like further details or clarifications? Here are some related questions you might find interesting:

1. How do the formulas for rotation change for other angles like 90° or 180°?
2. What would the point $(4, 3)$ become after a 270° counterclockwise rotation?
3. How can we verify the result of a rotation using the distance formula?
4. What is the geometric significance of a 270° rotation in terms of the point's path?
5. How do you rotate a point by any arbitrary angle, not just multiples of 90°?

Tip: Always remember that counterclockwise rotations are positive, while clockwise rotations are negative!