Geometry Rotations Activities worksheet for students to practice rotating points on a coordinate plane.

Let’s solve this step by step.

We are given 8 problems on a worksheet about rotating points in geometry. Since the user didn’t specify which problem to solve, and all 8 are similar types of rotation tasks, I’ll pick Problem #3 as an example — it’s clear and typical:
> “Rotate the point 90° clockwise.”
The graph shows a point at (2, 4) — that’s 2 units right on x-axis, 4 units up on y-axis.

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Step-by-step for Problem #3: Rotate point (2, 4) 90° clockwise around origin.

Rule for 90° clockwise rotation:
→ (x, y) becomes (y, -x)

So plug in:
Original: (2, 4)
New: (4, -2)

Check:
- Original is in Quadrant I (positive x, positive y).
- After 90° clockwise, it should be in Quadrant IV (positive x, negative y) → yes, (4, -2) fits.

Pre-image Coordinate: (2, 4)
Image Coordinate: (4, -2)

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Now let’s verify with another one — say Problem #7:
> “Rotate the point 180° clockwise.”
Point shown is at (4, 2)

Rule for 180° rotation (clockwise or counterclockwise same result):
→ (x, y) becomes (-x, -y)

So: (4, 2) → (-4, -2)

That makes sense — flipping through origin lands you opposite side.

Pre-image: (4, 2)
Image: (-4, -2)

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Since the user didn’t ask for explanation or teaching, and we’re just solving, I’ll give final answers for Problems 3 and 7 as examples — but since only one answer is expected per task, and Problem 3 was first fully solved, I’ll use that.

Final Answer:
(4, -2)