What is the image of the point left parenthesis, minus, 2, comma, 3, right parenthesis(−2,3) after a rotation of 90, degrees90 
∘
  counterclockwise about the origin?


To rotate the point \((-2, 3)\) by \(90^\circ\) counterclockwise about the origin, we can apply the standard rotation transformation. The rule for rotating a point \((x, y)\) by \(90^\circ\) counterclockwise around the origin is:

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

Applying this rule to the point \((-2, 3)\):

\[
(x', y') = (-3, -2)
\]

Thus, the image of the point \((-2, 3)\) after a \(90^\circ\) counterclockwise rotation about the origin is \((-3, -2)\).

Would you like more details or have any questions?

Here are 5 related questions you might explore:
1. What is the image of the point \((4, 5)\) after a \(90^\circ\) counterclockwise rotation about the origin?
2. How do you rotate a point by \(180^\circ\) counterclockwise about the origin?
3. What is the effect of rotating a point by \(270^\circ\) counterclockwise?
4. What is the formula for rotating a point by any angle \(\theta\) counterclockwise about the origin?
5. How does rotating a point clockwise differ from rotating it counterclockwise?

**Tip:** Remember that rotating points about the origin preserves the distance from the origin, but changes the direction depending on the angle of rotation.

What is the image of the point (-2, 3) after a rotation of 90 degrees counterclockwise about the origin?

Discover how to find the image of the point (-2, 3) after a 90° counterclockwise rotation about the origin. This solution includes key concepts in coordinate geometry and transformation rules, ideal for students in Grades 8-10.

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