This worksheet features 12 problems where students must rotate various geometric shapes around a specific point based on given angles and directions.

Let’s go through each problem one by one. We’re rotating shapes around a red star point on a grid. The direction (clockwise or anti-clockwise) and angle (90° or 180°) are given for each.

We’ll imagine turning the shape around that red dot like it’s pinned there — just like spinning a paper cutout with a pin in it.

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Problem 1:
Shape: Blue right triangle, pointing left.
Rotation: 90° clockwise about the red star (which is at the bottom-right corner of the triangle).
→ After rotating 90° clockwise, the triangle will point downward.
Final position: Right angle still at the star, but now the long side goes down instead of left.

Problem 2:
Shape: Yellow inverted triangle (pointing down), red star is at its top-right vertex.
Rotation: 90° clockwise.
→ Rotating this 90° clockwise makes it point to the right.
The star stays fixed; the whole triangle turns so the base becomes vertical on the right.

Problem 3:
Shape: Red right triangle, pointing left, red star at top end of vertical leg.
Rotation: 90° clockwise.
→ Turns so it points downward. The vertical leg becomes horizontal going right from the star.

Problem 4:
Shape: Small red triangle pointing left, red star at its rightmost tip.
Rotation: 90° anti-clockwise.
→ Turning counter-clockwise 90° makes it point upward.

Problem 5:
Shape: Blue inverted triangle (pointing down), red star at top-left vertex.
Rotation: 90° anti-clockwise.
→ Turns to point left. The base becomes vertical on the left side.

Problem 6:
Shape: Green right triangle pointing up, red star at bottom-right corner.
Rotation: 90° anti-clockwise.
→ Turns to point left. The vertical leg becomes horizontal going left from the star.

Problem 7:
Shape: Green “V” shape (like an arrowhead pointing down), red star at the bottom point.
Rotation: 180° anti-clockwise (same as 180° clockwise — flips it upside down).
→ Now it points upward. The V opens upward.

Problem 8:
Shape: Yellow irregular quadrilateral (looks like a house roof + wall), red star at top-left corner.
Rotation: 180° clockwise.
→ Flip it completely over the star. What was top-left becomes bottom-right relative to the star. Shape ends up mirrored diagonally across the star.

Problem 9:
Shape: Red parallelogram slanting up-right, red star at top-right corner.
Rotation: 180° anti-clockwise.
→ Flip it 180° — now it slants down-left from the star.

Problem 10:
Shape: Blue trapezoid standing vertically, red star at bottom-left corner.
Rotation: 90° anti-clockwise.
→ Turns to lie horizontally, opening to the left. The tall side becomes the bottom edge.

Problem 11:
Shape: Red L-shape (like a corner), red star at inner corner (bottom-left of the L).
Rotation: 90° clockwise.
→ Turns so the short arm goes down and the long arm goes right — looks like a backwards L rotated.

Actually, let’s visualize:
Original L: vertical part going up, horizontal part going right → after 90° CW rotation about the inner corner:
Vertical part becomes horizontal going left, horizontal part becomes vertical going down → forms an L pointing down-left.

Wait — better way: Imagine the L has two arms: one up, one right. Rotate 90° CW around the corner where they meet → now one arm goes right, one goes down → same orientation? No!

Actually, if you rotate the entire L 90° clockwise around the inner corner, the arm that was going UP will now go RIGHT, and the arm that was going RIGHT will now go DOWN. So it becomes an L shape with arms going right and down — which looks like the original but flipped.

But since the star is at the inner corner, yes — final shape has one segment extending right, one extending down from the star.

Problem 12:
Shape: Yellow U-shape (open at top), red star at bottom-left outer corner.
Rotation: 90° anti-clockwise.
→ Turn the whole U 90° CCW around that corner.
Originally, the U opens upward. After 90° CCW, it will open to the left.
The star is at the bottom-left — after rotation, that point stays, and the U now extends upward and rightward from it, opening left.

Wait — let's think carefully:

Original U: imagine three squares wide, two high, missing middle top square. Star is at bottom-left corner of the whole shape.

After 90° anti-clockwise rotation about that corner:
- The bottom row (horizontal) becomes a left column (vertical) going up.
- The right side (vertical) becomes a bottom row going left? Wait no.

Better: Each point rotates 90° CCW around the star.

So the shape that was sitting to the right and above the star will now be above and to the left of the star.

Specifically, the U that opened upward will now open to the left.

Yes — final shape: U opening to the left, with the star at what was originally the bottom-left, now becoming the top-left of the new orientation? Let me sketch mentally.

Actually, when you rotate 90° CCW around the bottom-left corner:
- The bottom edge (going right) becomes a left edge (going up).
- The left edge (going up) becomes a top edge (going left).
So the U, which had a base at bottom and sides going up, now has a base on the left and sides going right — meaning it opens to the right? I’m getting confused.

Alternative method: Use coordinates.

Assume star is at (0,0).

For Problem 12: Original U-shape — let’s say it occupies:
From x=0 to x=3, y=0 to y=2, but missing the center top: so cells (1,1) and (2,1) are empty? Actually, typical U: bottom row full (y=0, x=0,1,2), then sides at x=0,y=1 and x=2,y=1, and maybe x=0,y=2 and x=2,y=2? But usually simple U is 3 units wide, 2 high, with middle top missing.

To simplify: suppose the U consists of points:
(0,0), (1,0), (2,0), (0,1), (2,1), (0,2), (2,2) — but that’s not standard. Standard U might be: bottom: (0,0),(1,0),(2,0); left side: (0,1),(0,2); right side: (2,1),(2,2). So 7 cells.

Star is at (0,0).

Rotate each point 90° anti-clockwise around (0,0): rule is (x,y) → (-y,x)

So:
(0,0) → (0,0)
(1,0) → (0,1)
(2,0) → (0,2)
(0,1) → (-1,0)
(2,1) → (-1,2)
(0,2) → (-2,0)
(2,2) → (-2,2)

Now plot these:
New points: (0,0), (0,1), (0,2), (-1,0), (-1,2), (-2,0), (-2,2)

This looks like a U opening to the right? Because we have columns at x=-2, x=-1, x=0, with gaps in the middle at y=1 for x=-1 and x=0? Wait no.

At x=0: y=0,1,2 → full column
At x=-1: y=0 and y=2 → missing y=1
At x=-2: y=0 and y=2 → missing y=1

So it’s like a U lying on its side, opening to the right? But the "base" is at x=0, and the arms extend left to x=-1 and x=-2, with tops at y=2 and bottoms at y=0.

Actually, this is a U shape opening to the right, with the star at the bottom-right corner of the new shape? Since (0,0) is included, and it’s the rightmost point at bottom.

In terms of appearance: it should look like a U rotated 90° CCW, so if original opened up, now it opens left? But according to calculation, it opens right.

I think I made a mistake in coordinate system.

Standard math coordinates: x right, y up. But in grids for such worksheets, often y increases downward? Or upward?

In most school grids for transformations, the grid has rows increasing downward, like matrix notation. But for rotation, we need to be consistent.

Actually, in Cazoom worksheets, the grid is Cartesian with y increasing upward, I believe. But to avoid confusion, let's use visual reasoning.

Simple way: Take a piece of paper, draw the U with star at bottom-left. Pin it at star. Turn the paper 90° counter-clockwise. What happens?

The U that was sitting with open end up, after turning CCW 90°, the open end will face left. And the star, which was at bottom-left, is now at top-left of the new orientation? No.

When you rotate the paper CCW 90°, the bottom-left corner (star) stays, but the shape moves: the part that was to the right of the star is now above it, and the part that was above the star is now to the left of it.

So the U, which extended right and up from the star, now extends up and left from the star. And since it was open at the top, now it's open at the left.

Yes! So final shape: U opening to the left, with the star at the bottom-right corner of the U? Let's see:

Original: star at bottom-left. U goes right along bottom, and up along left side.

After 90° CCW rotation:
- The bottom edge (going right) becomes a left edge (going up) — so from star, it goes up.
- The left edge (going up) becomes a top edge (going left) — so from the top of that, it goes left.

So the U now has: from star, go up (this was the bottom), then at the top, go left (this was the left side), and similarly on the other side.

Actually, it's easier to accept that rotating a U 90° CCW around its bottom-left corner results in a U that opens to the left, with the star at the bottom-right corner of the new U shape.

But in our case, the star is fixed, so in the new position, the star is at what was the bottom-left, which after rotation is still the reference point.

Perhaps for the answer, we can describe the final orientation.

Since this is a worksheet, the expected answer is the drawn shape, but since we're describing, we'll state the orientation.

For all problems, the key is to apply the rotation correctly.

Let me list the final orientations clearly:

1) Triangle points down
2) Triangle points right
3) Triangle points down
4) Triangle points up
5) Triangle points left
6) Triangle points left
7) V points up
8) Quadrilateral flipped 180° — symmetric opposite
9) Parallelogram slants down-left
10) Trapezoid lies horizontally, opening left
11) L-shape: arms go right and down from star
12) U-shape opens to the left

Now, to confirm, let's double-check a few.

For Problem 11: L-shape, star at inner corner. Original: assume it has a vertical segment up and horizontal segment right from star. After 90° clockwise rotation: the up segment becomes right, the right segment becomes down. So from star, one arm goes right, one goes down — so it's an L with the corner at star, opening down-right. Yes.

For Problem 12: U-shape, star at bottom-left. After 90° anti-clockwise: the shape that was to the east and north of star is now north and west of star. The open top is now open left. So yes, U opens left.

All seem consistent.

Final Answer:
The rotated shapes are as follows:
1) Points downward
2) Points rightward
3) Points downward
4) Points upward
5) Points leftward
6) Points leftward
7) Points upward (inverted V)
8) Flipped 180° (mirror image through star)
9) Slants downward to the left
10) Lies horizontally, opening left
11) Arms extend right and down from star
12) Opens to the left