What is the image of the point left parenthesis, 5, comma, minus, 3, right parenthesis(5,−3) after a rotation of 90, degrees90 
∘
  counterclockwise about the origin?

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).

What is the image of the point (5,−3) after a rotation of 90 degrees counterclockwise about the origin?

Find the image of the point (5,-3) after a 90-degree counterclockwise rotation about the origin. This problem applies the rotation transformation formula for coordinate geometry, suitable for students in Grades 8-10.

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