What is the image of the point left parenthesis, 8, comma, minus, 9, right parenthesis(8,−9) after a rotation of 90, degrees90 
∘
  counterclockwise about the origin?


To perform a 90° counterclockwise rotation of a point \((x, y)\) about the origin, we use the following transformation rule:

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

For the point \((8, -9)\), apply this rule:

\[
(x', y') = (-(-9), 8) = (9, 8)
\]

So, the image of the point \((8, -9)\) after a 90° counterclockwise rotation about the origin is \((9, 8)\).

Would you like more details or have any questions?

Here are 5 related questions to further explore:
1. What is the image of the point \((8, -9)\) after a 180° rotation about the origin?
2. What is the image of the point \((8, -9)\) after a reflection over the y-axis?
3. How do you rotate a point 270° counterclockwise around the origin?
4. What happens to a point after a 90° clockwise rotation about the origin?
5. Can you explain the transformation rule for rotating a point 180°?

**Tip**: Always double-check the sign of the coordinates after rotation, as they often change depending on the angle and direction of the rotation.

What is the image of the point (8, -9) after a rotation of 90° counterclockwise about the origin?

Discover how to rotate the point (8, -9) 90 degrees counterclockwise around the origin. Using key geometric concepts and the formula (x', y') = (-y, x), this solution provides a clear transformation process for middle to high school students.

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