To find the image of a point after a $90^\circ$ counterclockwise rotation about the origin, we can use the following rule:

• The image of $(x, y)$ after a $90^\circ$ counterclockwise rotation becomes $(-y, x)$.

Given the point $(-3, 5)$, we apply this transformation:

$(x, y) = (-3, 5) \quad \rightarrow \quad (-y, x) = (-5, -3)$

So, the image of the point $(-3, 5)$ after a $90^\circ$ counterclockwise rotation about the origin is $(-5, -3)$.

Would you like more details or have any questions? Here are some related questions:

1. What is the formula for rotating a point $180^\circ$ about the origin?
2. How would you rotate a point $270^\circ$ counterclockwise about the origin?
3. What is the image of the point $(4, -2)$ after a $90^\circ$ counterclockwise rotation?
4. How do you reflect a point across the x-axis and y-axis?
5. How would you describe a $90^\circ$ clockwise rotation about the origin?

Tip: To remember rotations, it's helpful to visualize the coordinate plane and imagine moving counterclockwise or clockwise around the origin.