To find the image of the point $(5, -3)$ after a 90-degree counterclockwise rotation about the origin, we can apply the following transformation rule for rotating a point $(x, y)$ by 90 degrees counterclockwise:

$(x, y) \rightarrow (-y, x)$

Given the point $(5, -3)$:

1. The x-coordinate becomes the negative of the y-coordinate: $-(-3) = 3$
2. The y-coordinate becomes the x-coordinate: $5$

Thus, the image of the point $(5, -3)$ after the 90-degree counterclockwise rotation is:

$(3, 5)$

Would you like more details or further explanation?

Here are 5 related questions for practice:

1. What is the image of the point $(-4, 7)$ after a 90-degree clockwise rotation?
2. How do you find the image of a point after a 180-degree rotation?
3. What happens to the point $(x, y)$ after a 270-degree counterclockwise rotation?
4. Can you derive the transformation for a 45-degree rotation about the origin?
5. What is the image of the point $(2, -6)$ after a reflection over the x-axis?

Tip: For rotations, always remember to treat the point's coordinates according to the angle's direction and magnitude (clockwise or counterclockwise).