Consider the ordered pair G(6,-3). Determine the ordered pair for G' after a rotation of each of the following clockwise rotations: 90,180,270

To find the coordinates of the point \( G' \) after rotating \( G(6, -3) \) clockwise by 90°, 180°, and 270°, we use the following rotation rules for each case around the origin:

1. **90° clockwise rotation**:
   \[
   (x', y') = (y, -x)
   \]
   Substituting \( G(6, -3) \) into the formula:
   \[
   G'(90^\circ) = (-3, -6)
   \]

2. **180° clockwise rotation**:
   \[
   (x', y') = (-x, -y)
   \]
   Substituting \( G(6, -3) \) into the formula:
   \[
   G'(180^\circ) = (-6, 3)
   \]

3. **270° clockwise rotation**:
   \[
   (x', y') = (-y, x)
   \]
   Substituting \( G(6, -3) \) into the formula:
   \[
   G'(270^\circ) = (3, 6)
   \]

### Summary:
- \( G'(90^\circ) = (-3, -6) \)
- \( G'(180^\circ) = (-6, 3) \)
- \( G'(270^\circ) = (3, 6) \)

Would you like more details on rotation transformations, or have any questions?

Here are some related questions:
1. What is the general formula for a counterclockwise rotation?
2. How do you rotate a point around a different center instead of the origin?
3. What happens if the point is rotated clockwise by 360°?
4. Can you perform rotations using matrices?
5. How can you apply this rotation rule to geometric shapes like triangles or rectangles?

**Tip**: Always remember that clockwise and counterclockwise rotations have opposite effects!

Learn how to determine the coordinates of point G(6,-3) after a clockwise rotation of 90°, 180°, and 270°. This solution explains the rules for rotating points on the coordinate plane, providing formulas for each rotation angle. Suitable for students in Grades 8-10 studying geometry and transformations.

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