Geometry worksheet for practicing rotations of shapes on a grid, featuring 12 problems with various angles and directions.

To solve these rotation problems, we need to move each shape around the red cross (the center of rotation) according to the instructions.

Here is the step-by-step logic for how to rotate shapes:
1. Identify Key Points: Pick the corners (vertices) of the shape.
2. Count Squares: Count how many squares right/left and up/down each corner is from the red cross.
3. Rotate the Distance:
* 90° Clockwise: If a point is $x$ right and $y$ up, it moves to $x$ down and $y$ right. (Think: Right $\rightarrow$ Down, Up $\rightarrow$ Right).
* 90° Anti-clockwise: If a point is $x$ right and $y$ up, it moves to $x$ up and $y$ left. (Think: Right $\rightarrow$ Up, Up $\rightarrow$ Left).
* 180°: The shape ends up on the exact opposite side. If a point is $x$ right and $y$ up, it moves to $x$ left and $y$ down. It looks like the shape has been turned upside down.

Let's apply this to each question:

1) Blue Triangle: 90° Clockwise
* The vertical side is 2 units long and sits on the vertical line above the cross. Rotating "Up" 90° clockwise makes it go "Right". So, the new vertical side becomes a horizontal line going 2 units to the right of the cross.
* The top corner is 3 units left and 2 units up from the cross. Rotating this: "Left 3" becomes "Up 3", and "Up 2" becomes "Right 2". So the new corner is 2 units right and 3 units up.
* Result: A triangle with a horizontal base on the grid line above the cross? No, let's re-verify.
* Point A (on cross): Stays at cross.
* Point B (top of vertical leg): 2 units Up. Rotates to 2 units Right.
* Point C (far left tip): 3 units Left, 2 units Up.
* Rule for 90° CW $(x,y) \rightarrow (y, -x)$. Let Cross be $(0,0)$.
* Point C is $(-3, 2)$. New coords: $(2, 3)$. That is 2 Right, 3 Up.
* So, draw a line from the cross 2 units Right. Then go up 3 units from there? No, connect the points.
* The new shape has vertices at: The Cross, (2,0), and (2,3). It is a right-angled triangle standing vertically to the right of the cross.

2) Yellow Triangle: 90° Clockwise
* Top edge is horizontal, 3 units long, ending at the cross.
* Rotating "Left 3" (the edge) 90° clockwise makes it go "Up 3". So the new top edge is vertical, going 3 units up from the cross.
* The bottom tip is 1 unit down and 1.5 units left? Let's look closer. It looks like an isosceles triangle. The base is 3 units wide. The height is 2 units.
* Let's track the bottom tip. It is 1.5 units left and 2 units down from the midpoint of the base? Actually, let's just look at the vertices relative to the cross.
* Vertex 1 (at cross): $(0,0)$.
* Vertex 2 (left end of top edge): $(-3, 0)$. Rotates to $(0, 3)$ [3 Up].
* Vertex 3 (bottom tip): It is 1.5 units left and 2 units down from the cross? No, looking at the grid, the tip aligns with the middle of the 3-unit base. So it is 1.5 left? Grid lines are integers. Let's assume the vertices are on grid intersections.
* Looking closely at Q2: The top edge spans 3 squares. The cross is at the right end. The bottom vertex is 1 square left and 2 squares down from the cross? No, it looks like it's 1.5. Wait, usually these are integer coordinates. Let's look at the slope. From the right end (cross), go left 1, down 2? No, that would make the base 2. The base is 3.
* Let's assume the bottom vertex is at $(-1.5, -2)$. This is tricky on grids. Let's look at Q1 again. Q1 vertices were clearly on intersections. Q2: The bottom tip is exactly in the middle of the column? No, it looks like it's on a grid line intersection. Let's re-examine.
* Ah, the cross is at the right corner of the top edge. The top edge goes Left 3 units. The bottom vertex is 1 unit Left and 2 units Down from the cross? If so, the left vertex is $(-3,0)$, right is $(0,0)$, bottom is $(-1,-2)$? That doesn't look symmetric.
* Let's look at the shape again. It's an inverted triangle. Base on top. The cross is at the right end of the base. The base is 3 units long. The height is 2 units. The bottom vertex is horizontally centered relative to the base. Center of base is 1.5 units left. So the vertex is at $x=-1.5$. This implies half-grid squares.
* Okay, let's just rotate the visual orientation.
* Current: Pointing Down. Base is Horizontal.
* Rotate 90° Clockwise: Will Point Left. Base will be Vertical.
* The vertical base will start at the cross and go UP 3 units.
* The tip will stick out to the LEFT.
* Result: A triangle pointing left, with a vertical side of length 3 going up from the cross.

3) Purple Triangle: 90° Clockwise
* Shape: Right-angled triangle. Vertical side goes UP 2 units from a point. Horizontal side goes LEFT 2 units. The right angle is at the top-left? No.
* Let's trace from the cross. The cross is below the shape.
* The bottom vertex of the triangle is 1 unit Up and 0 Left/Right? No.
* Let's identify vertices relative to the cross $(0,0)$.
* Bottom-most vertex of triangle: $(0, 1)$? No, there is a gap. The cross is at a grid intersection. The triangle's bottom vertex is 1 unit Up and 0 horizontal? It looks like the vertical side of the triangle is on the same vertical line as the cross.
* Let's assume the vertical side is on the y-axis. The bottom of that side is at $(0,1)$. The top is at $(0,3)$. Length 2.
* The third vertex is to the left. At $(-2, 1)$.
* So vertices are $(0,1), (0,3), (-2,1)$.
* Rotate 90° Clockwise $(x,y) \rightarrow (y, -x)$.
* $(0,1) \rightarrow (1, 0)$. [1 Right]
* $(0,3) \rightarrow (3, 0)$. [3 Right]
* $(-2,1) \rightarrow (1, 2)$. [1 Right, 2 Up]
* Result: A triangle with a horizontal base on the line $y=0$ (same level as cross)? No, $y$ coordinate is the first number in $(y,-x)$? Standard math notation is $(x,y)$. Rotation 90 CW maps $(x,y)$ to $(y, -x)$.
* Old $x$ becomes new $-y$? No.
* Let's use the "Right/Up" logic.
* Point $(0,1)$ [1 Up] $\rightarrow$ 1 Right $(1,0)$.
* Point $(0,3)$ [3 Up] $\rightarrow$ 3 Right $(3,0)$.
* Point $(-2,1)$ [2 Left, 1 Up] $\rightarrow$ 2 Up, 1 Right $(1,2)$.
* So the new shape has vertices at $(1,0), (3,0), (1,2)$.
* This is a right-angled triangle sitting on the horizontal axis to the right of the cross. The vertical side is at $x=1$, going from $y=0$ to $y=2$. The horizontal side is at $y=0$, going from $x=1$ to $x=3$.

4) Green Triangle: 90° Anti-clockwise
* Vertices relative to cross:
* Rightmost vertex (at cross? No, cross is to the left).
* The cross is at the left tip of the triangle? No, the cross is 1 unit left of the triangle's left tip.
* Let's look really closely at crop 4. The red cross is at a grid intersection. The green triangle's left vertex is 1 unit Right of the cross.
* So Left Vertex: $(1,0)$.
* The triangle is right-angled? It looks like it. Vertical side on the right.
* Right Vertical Side is at $x=3$? (Length 2 units?). Let's assume the base is on the x-axis.
* Vertices: $(1,0), (3,0), (3,2)$. (Base length 2, Height 2).
* Rotate 90° Anti-clockwise. Rule: $(x,y) \rightarrow (-y, x)$. Or: Right $\rightarrow$ Up, Up $\rightarrow$ Left.
* $(1,0)$ [1 Right] $\rightarrow$ 1 Up $(0,1)$.
* $(3,0)$ [3 Right] $\rightarrow$ 3 Up $(0,3)$.
* $(3,2)$ [3 Right, 2 Up] $\rightarrow$ 3 Up, 2 Left $(-2,3)$.
* Result: A triangle with a vertical side on the y-axis (vertical line through cross) going from 1 Up to 3 Up. The third vertex is 2 units Left of that top point. So it points Left-Up.

5) Pink Triangle: 90° Anti-clockwise
* Cross is at the top-left vertex.
* Top edge is horizontal, going Right 3 units. Vertex at $(3,0)$.
* Bottom vertex: Looks like $x=1.5, y=-2$? Or is it integer? Let's assume standard integer grid problems. Maybe the vertex is $(1,-2)$ or $(2,-2)$?
* Looking at the slope, if it goes from $(0,0)$ to $(3,0)$ and the third point is $(1.5, -2)$, it's isosceles.
* Let's just rotate the orientation.
* Current: Points Down. Flat top.
* Rotate 90° Anti-clockwise: Points Right. Flat side becomes Vertical on the Left.
* The vertical side starts at the cross and goes DOWN? No.
* Top edge (Right 3) rotates Anti-clockwise to become Up 3.
* So the flat side is now vertical, going UP 3 units from the cross.
* The triangle points to the RIGHT.
* Result: A triangle with a vertical base on the line above the cross, extending 3 units up. The tip points to the right.

6) Blue Triangle: 90° Anti-clockwise
* Cross is at the bottom-left vertex of the bounding box?
* Let's trace vertices from cross $(0,0)$.
* Bottom vertex of triangle is at $(0,1)$? No, the cross is at the bottom-left corner of the triangle's position?
* Looking at crop 6: The cross is at the bottom-left vertex of the triangle.
* Vertical side goes UP 3 units. Vertex $(0,3)$.
* Horizontal side goes RIGHT 2 units? No, it's a right triangle. The hypotenuse connects them.
* Wait, the right angle is at the bottom-right?
* Let's assume vertices are $(0,0)$ [Cross], $(0,3)$ [Top], and $(2,0)$ [Right]? No, the shape is filled.
* The shape shown has a vertical side on the left and a horizontal side on the bottom? No, the cross is at the bottom-left corner of the *grid area*, but the triangle is shifted?
* Let's look at the red cross position relative to the blue shape. The cross is at the bottom-left vertex of the triangle.
* The triangle has a vertical side going UP 3 units. And a horizontal side going RIGHT 2 units? No, looking at the slope, it connects $(0,3)$ and $(2,0)$? That would be a right triangle with legs 3 and 2.
* Let's assume vertices: $(0,0), (0,3), (2,0)$ is wrong because the right angle symbol isn't there, but grid alignment suggests it. Actually, looking at the fill, the right angle is at the bottom-right? No.
* Let's assume the vertices are $(0,0)$ [Cross], $(0,3)$ [Top], and $(2,3)$? No.
* Let's look at the shape: It's a right triangle. Vertical leg is 3 units. Horizontal leg is 2 units. The right angle is at the top? No.
* Okay, simplest interpretation: The cross is at the bottom-left vertex. The vertical side goes up 3. The horizontal side goes right 2. The hypotenuse connects them. This assumes the right angle is at the cross? No, the line goes from cross up, and cross right?
* Actually, looking at Crop 6, the vertical line of the triangle is NOT on the cross's vertical line. The cross is to the left of the triangle.
* Correction: The cross is at $(0,0)$. The triangle's bottom-left vertex is at $(1,1)$? No.
* Let's look at the grid lines. The cross is at an intersection. The triangle's bottom vertex is 1 unit Right and 1 unit Up?
* Let's try again. Look at the vertical line of the triangle. It is 1 unit to the right of the cross. The bottom of that line is 1 unit up from the cross.
* So Bottom-Right vertex of triangle is at $(1,1)$.
* Top vertex is at $(1,4)$ (3 units high).
* Left vertex is at... wait, it's a right triangle. The right angle is at the bottom-right $(1,1)$. The other leg goes Left 2 units to $(-1,1)$? No, that crosses the y-axis.
* Let's look at the image again very carefully.
* Crop 6: Red cross. To its right, one square gap? No. The triangle starts 1 unit right of the cross. The bottom of the triangle is 1 unit up from the cross.
* So the bottom-right corner of the triangle is at $(1,1)$.
* The vertical side goes up 3 units to $(1,4)$.
* The horizontal side goes left 2 units to $(-1,1)$? No, the triangle is to the right of the cross.
* Let's assume the vertices are $(1,1), (1,4), (3,1)$. Right angle at $(1,1)$? No, hypotenuse is on the left?
* Okay, let's look at the slope. The slanted side is on the left. The vertical side is on the right.
* So vertices: Right-Bottom $(3,1)$, Right-Top $(3,4)$, Left-Bottom $(1,1)$?
* Let's count grid squares from the cross.
* Cross is at $(0,0)$.
* Triangle bottom edge is on line $y=1$.
* Triangle left edge is on line $x=1$? No, the slanted side starts at $x=1, y=1$ and goes to $x=3, y=4$?
* Let's assume the standard simple case: The cross is the center of rotation.
* Let's pick the closest point on the shape to the cross. It looks like the bottom-left tip of the triangle is at $(1,1)$.
* The top tip is at $(1,4)$? No, if it's a right triangle with vertical/horizontal legs, and the slant is on the left, then the vertical leg is on the right.
* Let's assume vertices: $(1,1), (3,1), (3,4)$. Right angle at $(3,1)$.
* Rotate 90° Anti-clockwise.
* $(1,1)$ [1R, 1U] $\rightarrow$ 1L, 1U $\rightarrow (-1,1)$.
* $(3,1)$ [3R, 1U] $\rightarrow$ 1L, 3U $\rightarrow (-1,3)$.
* $(3,4)$ [3R, 4U] $\rightarrow$ 4L, 3U $\rightarrow (-3,3)$.
* Result: A triangle in the top-left quadrant. Vertical side on the left?
* New points: $(-1,1), (-1,3), (-3,3)$.
* Segment $(-1,1)$ to $(-1,3)$ is vertical, length 2.
* Segment $(-1,3)$ to $(-3,3)$ is horizontal, length 2.
* This forms a right triangle with right angle at $(-1,3)$.

7) Yellow Arrowhead: 180°
* Cross is at the bottom tip.
* Shape points Up.
* Rotate 180°: Shape points Down.
* The "wings" which were Up-Left and Up-Right will now be Down-Right and Down-Left.
* Result: An arrowhead pointing straight down, with the tip at the cross.

8) Purple Kite/Diamond: 180°
* Cross is at the left vertex.
* Shape extends to the Right and Up/Down.
* Rotate 180°: The shape will extend to the Left and Down/Up (inverted vertically).
* Essentially, flip it horizontally and vertically.
* The right vertex will move to the left. The top vertex will move to the bottom.
* Result: A kite shape attached to the cross on its right side? No, attached on its right vertex?
* Original: Left vertex at cross. Right vertex far away.
* New: Right vertex at cross. Left vertex far away (to the left).
* So the shape hangs off the cross to the left, flipped upside down.

9) Green Parallelogram: 180°
* Cross is at the top-right vertex.
* Shape goes Down and Left.
* Rotate 180°: Shape goes Up and Right.
* Result: A parallelogram extending up and to the right from the cross. It will look like the original shape rotated upside down.

10) Blue Trapezium: 90° Anti-clockwise
* Cross is at the bottom-left vertex.
* Vertical side goes UP 4 units.
* Top side goes RIGHT 2 units?
* Slanted side connects back?
* Let's assume vertices: $(0,0)$ [Cross], $(0,4)$ [Top-Left], $(2,4)$ [Top-Right], $(2,1)$ [Bottom-Right]?
* Looking at crop 10: Vertical side on the left. Horizontal top. Slanted right side. Horizontal bottom? No, the cross is at the bottom tip of the slanted side?
* Let's look at the cross. It is at the bottom vertex of the shape.
* The side going up from the cross is slanted? No, the side to the left of the cross is empty. The shape is to the right.
* The vertex at the cross is the bottom-left of the bounding box?
* Let's assume the vertical side is NOT on the cross.
* Looking at the grid: The cross is at the bottom endpoint of the left-most vertical line? No, the left-most line is slanted?
* Actually, it looks like a trapezoid. Left side is vertical. Top is horizontal. Right side is slanted. Bottom is horizontal.
* Cross is at the bottom-left corner.
* So vertices: $(0,0), (0,4), (2,4), (3,0)$?
* Let's check the slope. From $(2,4)$ to $(3,0)$? That's steep.
* Let's assume simpler: Rectangle + Triangle?
* Let's just rotate the "L" shape of the left and top sides.
* Left side: Vertical, Up 4. Rotates Anti-clockwise $\rightarrow$ Horizontal, Left 4.
* Top side: Horizontal, Right 2 (from the top of the left side). Rotates Anti-clockwise $\rightarrow$ Vertical, Up 2 (from the left end of the new horizontal side).
* So the new shape has a horizontal base going 4 units Left from the cross. At the end of that base, a vertical line goes 2 units Up.
* The rest of the shape fills in accordingly.
* Result: The shape lies to the left of the cross.

11) Orange L-Shape: 90° Clockwise
* Cross is at the top-left corner of the L.
* Horizontal part goes Right 2. Vertical part goes Down 2.
* Rotate 90° Clockwise.
* "Right 2" becomes "Down 2".
* "Down 2" becomes "Left 2".
* So the new shape has a vertical part going Down 2 from the cross, and a horizontal part going Left 2 from the bottom of that vertical part.
* Result: An L-shape hanging down and to the left of the cross.

12) Purple U-Shape: 90° Anti-clockwise
* Cross is at the top-left corner.
* Shape goes Right, Down, Up, Right, Up? No, it's a U.
* Left arm goes Down. Bottom goes Right. Right arm goes Up.
* Rotate 90° Anti-clockwise.
* "Down" becomes "Right".
* "Right" becomes "Up".
* "Up" becomes "Left".
* So the Left Arm (originally Down) now points Right.
* The Bottom (originally Right) now points Up.
* The Right Arm (originally Up) now points Left.
* Result: A U-shape lying on its side, opening to the Left?
* Start at cross. Go Right (new left arm). Go Up (new bottom). Go Left (new right arm).
* Yes, it looks like a C shape or a U rotated. It opens to the left.

Final Answer Summary:
1. Triangle to the right of the cross, pointing up/right.
2. Triangle pointing left, vertical base going up from cross.
3. Triangle to the right, sitting on the horizontal line.
4. Triangle in top-left quadrant.
5. Triangle pointing right, vertical base going up from cross.
6. Triangle in top-left quadrant.
7. Arrowhead pointing down.
8. Kite shape to the left of the cross, inverted.
9. Parallelogram up and to the right.
10. Trapezium to the left of the cross.
11. L-shape down and to the left.
12. U-shape opening to the left.

Since I cannot draw, I will describe the final positions clearly.

Final Answer:

Here are the descriptions of the rotated shapes for each question:

1. 90° Clockwise: The triangle is now to the right of the cross. Its vertical side is now horizontal, and it points upwards.
2. 90° Clockwise: The triangle now points to the left. Its flat top edge is now a vertical line going up from the cross.
3. 90° Clockwise: The triangle is now to the right of the cross, sitting on the same horizontal line as the cross.
4. 90° Anti-clockwise: The triangle is now in the top-left area relative to the cross.
5. 90° Anti-clockwise: The triangle now points to the right. Its flat top edge is now a vertical line going up from the cross.
6. 90° Anti-clockwise: The triangle is now in the top-left area relative to the cross.
7. 180°: The arrowhead now points straight down.
8. 180°: The kite shape is now to the left of the cross and is upside down.
9. 180°: The parallelogram is now extending up and to the right from the cross.
10. 90° Anti-clockwise: The trapezium is now to the left of the cross.
11. 90° Clockwise: The L-shape is now hanging down and to the left of the cross.
12. 90° Anti-clockwise: The U-shape is now lying on its side, opening to the left.