What is the image of the point left parenthesis, minus, 1, comma, 7, right parenthesis(−1,7) after a rotation of 90, degrees90 
∘
  counterclockwise about the origin?

To find the image of the point \((-1, 7)\) after a 90° counterclockwise rotation about the origin, we can use the standard rotation rule for rotating a point \((x, y)\) by 90° counterclockwise:

\[
(x', y') = (-y, x)
\]

For the point \((-1, 7)\):
- The x-coordinate becomes \(-7\),
- The y-coordinate becomes \(-1\).

Thus, the new coordinates after the rotation are:

\[
\text{New point} = (-7, -1)
\]

The image of the point \((-1, 7)\) after a 90° counterclockwise rotation is \((-7, -1)\).

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Would you like further details on this rotation process or any clarifications?

### Related Questions:
1. What is the general formula for rotating a point by different angles?
2. How does the rotation change if it were clockwise instead?
3. Can you explain how to rotate a point around a point other than the origin?
4. How do you determine the distance between the original and rotated points?
5. What would happen if the point \((-1, 7)\) is reflected across the x-axis instead of rotated?

**Tip:** When rotating points, always visualize how the axes change and apply the correct transformation rule.

What is the image of the point (-1, 7) after a rotation of 90 degrees counterclockwise about the origin?

Discover how to find the image of the point (-1, 7) after a 90° counterclockwise rotation about the origin. Using the transformation rule (x', y') = (-y, x), this guide will help you understand coordinate rotations. Suitable for students in Grades 9-10.

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