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.