To determine the coordinates of point $G'$ after rotating the point $G(-2, -5)$ counterclockwise by 90°, 180°, 270°, and 360°, we use the following rules for rotation about the origin:

1. 90° Rotation (Counterclockwise):

   • Formula: $(x, y)$ → $(-y, x)$
   • For $G(-2, -5)$:
     $G' = (-(-5), -2) = (5, -2)$

2. 180° Rotation (Counterclockwise):

   • Formula: $(x, y)$ → $(-x, -y)$
   • For $G(-2, -5)$:
     $G' = (-(-2), -(-5)) = (2, 5)$

3. 270° Rotation (Counterclockwise):

   • Formula: $(x, y)$ → $(y, -x)$
   • For $G(-2, -5)$:
     $G' = (-5, 2)$

4. 360° Rotation (Counterclockwise):

   • Formula: $(x, y)$ → $(x, y)$ (No change in position)
   • For $G(-2, -5)$:
     $G' = (-2, -5)$

Summary of results:

• After 90° rotation: $G'(5, -2)$
• After 180° rotation: $G'(2, 5)$
• After 270° rotation: $G'(-5, 2)$
• After 360° rotation: $G'(-2, -5)$

Would you like a detailed explanation of how each transformation is derived, or do you have any other questions?

Here are 5 related questions to expand on this information:

1. What is the effect of rotating a point 90° clockwise around the origin?
2. How would you reflect the point $G(-2, -5)$ across the x-axis?
3. What are the coordinates of point $G(-2, -5)$ after a reflection over the y-axis?
4. How does a 180° rotation differ from a reflection across the origin?
5. How would you determine the coordinates after rotating around a point other than the origin?

Tip: When rotating points around the origin, always keep in mind the rules for how x and y coordinates switch places and change signs for each specific angle of rotation.