(-3,2) rotate 90 degrees CW rotate 180 degrees CW rotate 90 degrees CCW from orignal

Let's calculate the coordinates of the point (-3, 2) after each rotation:

### 1. **90 Degrees Clockwise (CW) Rotation:**
   To rotate a point \((x, y)\) 90 degrees clockwise, we use the transformation formula:
   \[
   (x', y') = (y, -x)
   \]
   For the point \((-3, 2)\):
   \[
   (x', y') = (2, 3)
   \]
   So, after a 90° CW rotation, the point is **(2, 3)**.

### 2. **180 Degrees Clockwise (CW) Rotation:**
   Rotating 180 degrees clockwise is the same as rotating 180 degrees counterclockwise. The formula is:
   \[
   (x', y') = (-x, -y)
   \]
   For the point \((-3, 2)\):
   \[
   (x', y') = (3, -2)
   \]
   So, after a 180° CW rotation, the point is **(3, -2)**.

### 3. **90 Degrees Counterclockwise (CCW) Rotation:**
   To rotate a point \((x, y)\) 90 degrees counterclockwise, we use the transformation formula:
   \[
   (x', y') = (-y, x)
   \]
   For the point \((-3, 2)\):
   \[
   (x', y') = (-2, -3)
   \]
   So, after a 90° CCW rotation, the point is **(-2, -3)**.

### Summary of Rotations:
1. 90° CW: \((2, 3)\)
2. 180° CW: \((3, -2)\)
3. 90° CCW: \((-2, -3)\)

Would you like more details on the rotation process or have any questions?

Here are five related questions:
1. What happens when a point is rotated 270° CW?
2. How do you rotate a point about a point other than the origin?
3. Can you describe how the distance from the origin changes after a rotation?
4. What transformation results from reflecting a point across both axes?
5. How would you rotate a point by 45°?

**Tip:** When performing multiple transformations, keeping track of the order is crucial, as rotations are not commutative.

(-3,2) rotate 90 degrees CW rotate 180 degrees CW rotate 90 degrees CCW from original

Explore how to rotate the point (-3, 2) by 90 degrees clockwise, 180 degrees clockwise, and 90 degrees counterclockwise. This problem covers key geometric transformations and provides step-by-step solutions, perfect for students in Grades 8-10.

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