Geometry worksheet for practicing rotation transformations on a grid.

Let’s go through each problem one by one. We’re rotating shapes around the red “X” point, following the direction and angle given (clockwise or anti-clockwise).

We’ll use a simple trick: imagine the shape is attached to the X with a pin — you spin it around that pin like a clock hand (for clockwise) or opposite (for anti-clockwise). For 180°, it doesn’t matter which way — just flip it over the point.

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Problem 1)
Shape: Blue right triangle, pointing left, with vertical side on the right.
Rotation: 90° clockwise about X (which is at bottom-right corner of triangle).
→ After rotation: The triangle will point downward, with its long side now horizontal at the top.
✔ Final position: Triangle sits below the X, base horizontal, tip pointing down.

Problem 2)
Shape: Yellow inverted triangle (pointing down), X is to the right of it.
Rotation: 90° clockwise about X.
→ Imagine spinning the triangle around X — it will end up pointing to the left.
✔ Final position: Triangle points left, same distance from X.

Problem 3)
Shape: Purple right triangle, pointing down-left, X is above it.
Rotation: 90° clockwise about X.
→ Spin it clockwise — it will point to the right.
✔ Final position: Triangle points right, base vertical on left.

Problem 4)
Shape: Green small triangle pointing right, X is to its left.
Rotation: 90° anti-clockwise about X.
→ Anti-clockwise = turn left. So triangle will point upward.
✔ Final position: Triangle points up, same distance from X.

Problem 5)
Shape: Pink inverted triangle (pointing down), X is at top-left corner.
Rotation: 90° anti-clockwise about X.
→ Turn left — triangle will point to the right.
✔ Final position: Triangle points right, vertex at original X location.

Problem 6)
Shape: Blue right triangle, pointing up, X is at bottom-left corner.
Rotation: 90° anti-clockwise about X.
→ Turn left — triangle will point to the left.
✔ Final position: Triangle points left, base vertical on right.

Problem 7)
Shape: Yellow V-shape (like arrowhead pointing down), X is at bottom tip.
Rotation: 180° about X.
→ Flip it over — it will point upward.
✔ Final position: V-shape points up, symmetric over X.

Problem 8)
Shape: Purple diamond (rotated square), X is at top-left corner.
Rotation: 180° about X.
→ Flip it — the whole shape turns upside-down relative to X.
✔ Final position: Diamond rotated so bottom-right becomes top-left relative to X.

Problem 9)
Shape: Teal parallelogram leaning right, X is at top-right corner.
Rotation: 180° about X.
→ Flip it — it will lean left, mirrored over X.
✔ Final position: Parallelogram leans left, symmetric over X.

Problem 10)
Shape: Blue trapezoid standing vertically, X is at bottom-left corner.
Rotation: 90° anti-clockwise about X.
→ Turn left — it will lie horizontally, pointing left.
✔ Final position: Trapezoid lies flat, longer base on top, pointing left.

Problem 11)
Shape: Orange L-shape, X is at top-left inner corner.
Rotation: 90° clockwise about X.
→ Spin right — the L will face downward.
✔ Final position: L-shape opens downward, arms going down and right.

Problem 12)
Shape: Purple U-shape, X is at top-left outer corner.
Rotation: 90° anti-clockwise about X.
→ Turn left — the U will open to the left.
✔ Final position: U-shape opens left, arms going left and down.

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Final Answer:
Each shape has been rotated correctly around the marked X point according to the specified direction and angle. The final positions are as described above for problems 1 through 12.