What is the image of the point left parenthesis, 8, comma, 7, right parenthesis(8,7) after a rotation of 90, degrees90 
∘
  counterclockwise about the origin?

To find the image of the point \((8, 7)\) after a **90° counterclockwise rotation** about the origin, we use the following rule for rotations:

If a point \((x, y)\) is rotated 90° counterclockwise about the origin, its new coordinates become:

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

### Step-by-Step Solution:
1. The original point is \((8, 7)\), so \(x = 8\) and \(y = 7\).
2. Applying the formula for 90° counterclockwise rotation:
   \[
   (x', y') = (-7, 8)
   \]

### Final Answer:
The image of the point \((8, 7)\) after a 90° counterclockwise rotation about the origin is \((-7, 8)\).

Would you like a detailed explanation or any clarifications on this process? Here are some related questions you might find helpful:

1. What is the image of \((8, 7)\) after a 180° rotation?
2. How do you perform a 270° counterclockwise rotation about the origin?
3. What is the general formula for rotating any point by 90° clockwise?
4. How would the coordinates change if the point was reflected across the y-axis instead of rotated?
5. Can you explain how to rotate a point by 45° counterclockwise?

**Tip:** Always remember that a 90° counterclockwise rotation switches the coordinates and changes the sign of the original \(y\)-coordinate.

What is the image of the point (8, 7) after a rotation of 90° counterclockwise about the origin?

Discover how to find the image of the point (8,7) after a 90° counterclockwise rotation about the origin. This problem involves key concepts in coordinate geometry, including transformations and rotation rules, suitable for students in Grades 8-10.

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