If point P(3, 2) is rotated 90 degree counterclockwise with respect to the origin, what will be its new coordinates ?

Options

A. `(-2, 3)`
B. `(-2, -3)`
C. `(-3, 3)`
D. `(-3, 2)`

Explanation

To find the new coordinates of point P(3, 2) after a 90-degree counterclockwise rotation about the origin, we can use the following steps:

### Step 1: Understand the rotation transformation
When a point (x, y) is rotated 90 degrees counterclockwise about the origin, the new coordinates (x', y') can be found using the transformation:
\[ x' = -y \]
\[ y' = x \]

### Step 2: Identify the original coordinates
The original coordinates of point P are:
\[ x = 3, \quad y = 2 \]

### Step 3: Apply the transformation
Now, we will apply the transformation to find the new coordinates:
1. Calculate \(x'\):
\[ x' = -y = -2 = -2 \]
2. Calculate \(y'\):
\[ y' = x = 3 \]

### Step 4: Write the new coordinates
After applying the transformation, the new coordinates of point P after the rotation are:
\[ P'(-2, 3) \]

### Conclusion
The new coordinates of point P(3, 2) after a 90-degree counterclockwise rotation about the origin are \((-2, 3)\).