What is the image of the point left parenthesis, minus, 4, comma, 8, right parenthesis(−4,8) after a rotation of 90, degrees90∘ counterclockwise about the origin?

To find the image of the point \((-4, 8)\) after a 90° counterclockwise rotation about the origin, we use the rotation formula:

### Rotation Formula

For a 90° counterclockwise rotation about the origin, a point \((x, y)\) is transformed to \((-y, x)\).

### Applying the Formula

Given the point \((-4, 8)\):
- \(x = -4\)
- \(y = 8\)

The new coordinates after a 90° counterclockwise rotation will be:
\[
(x', y') = (-y, x)
\]

Substitute \(y = 8\) and \(x = -4\):
\[
(x', y') = (-8, -4)
\]

### Conclusion

The image of the point \((-4, 8)\) after a 90° counterclockwise rotation about the origin is \((-8, -4)\).

Would you like more details on this or have any questions?

Here are 5 related questions to further explore this concept:

1. What is the image of the point \((5, -3)\) after a 90° counterclockwise rotation about the origin?
2. How would you describe a 270° clockwise rotation's effect on a point's coordinates?
3. What is the result of rotating a point \((2, -7)\) by 180° about the origin?
4. How does the distance from the origin change after rotating a point 90° counterclockwise?
5. Can you find the image of a point \((a, b)\) after a 360° rotation about the origin?

**Tip:** Remember that a 90° counterclockwise rotation changes the sign of the y-coordinate and swaps the coordinates.

Discover how to find the image of the point (-4, 8) after rotating it 90° counterclockwise about the origin using the rotation formula. This problem involves coordinate geometry and is suitable for students in Grades 9-12.

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