Centre of rotation & symmetry worksheets | shape translation - Free Printable
Educational worksheet: Centre of rotation & symmetry worksheets | shape translation. Download and print for classroom or home learning activities.
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Step-by-step solution for: Centre of rotation & symmetry worksheets | shape translation
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Show Answer Key & Explanations
Step-by-step solution for: Centre of rotation & symmetry worksheets | shape translation
Since the user did not select any specific options (ExplainAnswer, TeachTopic, or GeneratePractice are all false), I will provide the direct solutions to the tasks shown in the worksheets. The image contains three different rotation exercises. I will break them down by section.
Task: Complete the pattern by rotating the shape a quarter turn (90 degrees) in the direction of the arrow.
* Row 1: Triangle rotates clockwise → Arrow points Right.
* Row 2: Triangle rotates clockwise → Diamond (Square rotated). *Wait, looking closely at Row 2:* It starts with a triangle pointing up. The arrow is clockwise. The next shape is a diamond? No, that looks like a separate example. Let's look at the empty boxes.
* Row 3 (Heart): The heart is upright. The arrow shows a clockwise quarter turn. A heart rotated 90° clockwise will point to the right.
* Row 4 (Trapezoid): The trapezoid has the long side on the bottom. The arrow shows a counter-clockwise quarter turn. Rotating it 90° left means the long side will be on the right.
* Row 5 (Curved Line/Crescent): The curve opens to the top-left. The arrow is counter-clockwise. Rotating 90° left means the opening will face down-left.
* Row 6 (Triangle): The triangle points down. The arrow is clockwise. Rotating 90° right means the triangle will point left.
* Row 7 (Semi-circle): The flat side is on the left. The arrow is counter-clockwise. Rotating 90° left means the flat side will be on the bottom.
* Row 8 (Pentagon): The pentagon points up. The arrow is clockwise. Rotating 90° right means the point will face right.
*(Note: Since this is a visual pattern task, the "answer" is drawing the shapes described above.)*
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Task: Rotate the shaded shape according to the instructions.
Top Part: Quarter Turn Clockwise
1. Triangle: The hypotenuse goes from top-left to bottom-right. After a 90° clockwise turn, the right angle moves from bottom-left to top-left. The new triangle sits in the top-left corner of its bounding box.
2. L-Shape: The vertical part is on the left. After a 90° clockwise turn, the long part becomes horizontal on the top, and the short part hangs down on the right.
3. Rectangle: It is vertical (tall). After a 90° clockwise turn, it becomes horizontal (wide).
Bottom Part: Quarter Turn Anti-Clockwise (Counter-Clockwise)
1. Triangle: The right angle is at the bottom-left. Rotating 90° left moves the right angle to the bottom-right. The hypotenuse faces top-left.
2. L-Shape: The long part is vertical on the left. Rotating 90° left makes the long part horizontal on the bottom, with the short part sticking up on the left.
3. Arrow: Points right. Rotating 90° left makes it point up.
4. Rectangle: It is horizontal (wide). Rotating 90° left makes it vertical (tall).
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Task: Match the numbered shapes (1–8) to the correct instruction based on how they were rotated from the original bold shape.
Original Shapes & Matches:
1. Original: Pentagon (pointing up)
* Shape ①: Pointing left. This is a 90° anti-clockwise (or 270° clockwise) turn.
* *Instruction Match:* Look for "1/4 turn anti-clockwise".
2. Original: L-Shape (standing up, foot to right)
* Shape ②: Lying on back, foot up. This is a 90° anti-clockwise turn.
* Shape ⑤: Upside down. This is a 1/2 turn (180°).
* Shape ⑧: Standing up, foot to left. This is a reflection (flip), not a simple rotation in 2D plane unless specified, but usually these tests stick to rotations. Wait, let's look closer. Shape 8 is a mirror image. If only rotations are allowed, this might be a trick or I need to re-evaluate. Let's look at the other L-shapes.
* Actually, let's look at the instructions provided in the key at the bottom:
* 1/2 turn clockwise
* 1/4 turn clockwise
* 1/4 turn anti-clockwise
* 3/4 turn clockwise (which is same as 1/4 anti-clockwise)
Let's re-evaluate the matches based on standard rotations:
* Group 1: Pentagon
* Original: Point Up.
* Shape ①: Point Left. Rotation: 1/4 turn anti-clockwise (or 3/4 clockwise).
* Shape ④: Point Down-Right? No, Shape 4 is a triangle. Let's group by shape type.
Let's solve by matching each numbered item to its rotation description:
* Item ① (Pentagon pointing Left): From Up to Left is 1/4 turn anti-clockwise.
* Item ② (L-Shape lying down): Original L stands tall with foot right. Shape 2 lies on its back with foot up. This is a 1/4 turn anti-clockwise.
* Item ③ (Zig-Zag/Step shape): Original steps go down-right. Shape 3 steps go down-left. This looks like a reflection or a 1/2 turn? Let's trace it. Top block moves from top-left to bottom-right. This is a 1/2 turn.
* Item ④ (Triangle): Original right-angle triangle (hypotenuse top-left to bottom-right). Shape 4 has hypotenuse top-right to bottom-left. This is a 1/2 turn (180°) or reflection. In rotation terms, rotating 180° keeps the slope negative if it started negative? No.
* Let's visualize: Original triangle vertices roughly (0,1), (1,1), (1,0). Rotate 180 -> (0,-1), (-1,-1), (-1,0). The shape flips.
* Actually, simpler view: The right angle is at bottom-right in original. In Shape 4, the right angle is at top-left. This is a 1/2 turn.
* Item ⑤ (L-Shape upside down): Original stands tall. Shape 5 is upside down. This is a 1/2 turn.
* Item ⑥ (Arrow pointing Down-Left?): Original Arrow points Down. Shape 6 points Left. Down to Left is a 1/4 turn clockwise.
* Item ⑦ (Complex Step Shape): Original has a "C" cutout facing right. Shape 7 has the cutout facing left. This is a 1/2 turn.
* Item ⑧ (L-Shape mirrored?): Original foot right. Shape 8 foot left. This is a reflection. However, if we must choose a rotation, a 1/2 turn would make it upside down. A 1/4 turn would make it lie down. Shape 8 is upright. This implies the question might include reflections or "turns" in 3D? Or perhaps I am misidentifying the original.
* *Correction:* Look at the original L-shape again. It is an 'L'. Shape 8 is a backwards 'L'. This is a Flip (Reflection). If the worksheet strictly says "Rotation", there might be an error in my interpretation or the sheet includes flips.
* *Alternative:* Maybe Shape 8 is the result of a 1/4 turn clockwise followed by a flip? Unlikely.
* *Let's look at the remaining Triangle:*
* Item ⑨ (Triangle pointing Right): Original Hypotenuse \ . Shape 9 Hypotenuse / . Right angle at bottom-left. Original right angle at bottom-right. This is a 1/4 turn anti-clockwise?
* Original: Right angle bottom-right.
* Rotate 90° Anti-Clockwise: Right angle moves to bottom-left. Vertical side becomes horizontal bottom. Horizontal side becomes vertical left.
* Shape 9: Right angle is bottom-left. Vertical side is on the left. Horizontal side is on the bottom. Yes. Item 9 is 1/4 turn anti-clockwise.
Let's refine the Answers for the Right Sheet based on the visible numbers 1-8 (and 9 is cut off or part of another set? The image shows 1-8 clearly in boxes, and a 9th triangle on the far right).
Let's map the specific numbered boxes to the likely intended answers:
* Box 1 (Pentagon): Rotated 90° Left. Answer: 1/4 turn anti-clockwise.
* Box 2 (L-Shape): Rotated 90° Left. Answer: 1/4 turn anti-clockwise.
* Box 3 (Steps): Rotated 180°. Answer: 1/2 turn.
* Box 4 (Triangle): Rotated 180°. Answer: 1/2 turn.
* Box 5 (L-Shape): Rotated 180°. Answer: 1/2 turn.
* Box 6 (Arrow): Original points Down. Shape points Left. That is 90° Right (Clockwise). Answer: 1/4 turn clockwise.
* Box 7 (Blocky C-shape): Rotated 180°. Answer: 1/2 turn.
* Box 8 (Backwards L): As noted, this is a reflection. If forced to choose a rotation from standard options, it doesn't fit. However, looking at the layout, sometimes "Rotation" worksheets loosely use "Turn" to include flips in lower grades, OR I am missing a step.
* *Wait*, look at the original L-shape for #8. Is it possible the original was different? No, it's the same L as #2 and #5.
* Let's check 1/4 turn clockwise for L-shape: Original (Up/Foot-Right) -> 90° CW -> (Right/Foot-Down). That would look like an L lying on its face. That is not #8.
* Let's check 3/4 turn clockwise (same as 1/4 ACW): That is #2.
* There is no rotation that turns an L into a backwards L in 2D. It is a reflection. If the student must write a rotation, the question may be flawed, or "Flip" is an allowed answer despite the header "Rotation". Given the "Eco ink saving" label, this is likely a standard primary school sheet. Primary schools often teach Reflections separately. I will flag #8 as a Reflection/Flip.
* Box 9 (Triangle on far right): Right angle bottom-left. Original right angle bottom-right. This is 1/4 turn anti-clockwise.
Summary of Matches for the Right Worksheet:
* 1/4 turn clockwise: Shape 6 (Arrow)
* 1/4 turn anti-clockwise: Shape 1 (Pentagon), Shape 2 (L-Shape), Shape 9 (Triangle)
* 1/2 turn: Shape 3 (Steps), Shape 4 (Triangle), Shape 5 (L-Shape), Shape 7 (Blocky C)
* Reflection (Flip): Shape 8 (Backwards L)
Final Answer:
Here are the solutions to the problems in the image:
Left Worksheet (Drawing Patterns)
* Heart: Draw the heart pointing to the right.
* Trapezoid: Draw the trapezoid with the long parallel side on the right (vertical).
* Curved Line: Draw the curve opening towards the bottom-left.
* Triangle: Draw the triangle pointing to the left.
* Semi-circle: Draw the semi-circle with the flat edge on the bottom.
* Pentagon: Draw the pentagon with the point facing right.
Middle Worksheet (Grid Rotations)
* Top Row (Clockwise):
1. Triangle: Right angle moves to the top-left.
2. L-Shape: Long side is horizontal on top; short side hangs down on the right.
3. Rectangle: Becomes horizontal (wide).
* Bottom Row (Anti-Clockwise):
1. Triangle: Right angle moves to the bottom-right.
2. L-Shape: Long side is horizontal on the bottom; short side sticks up on the left.
3. Arrow: Points up.
4. Rectangle: Becomes vertical (tall).
Right Worksheet (Matching Instructions)
* Shape 1 (Pentagon): 1/4 turn anti-clockwise
* Shape 2 (L-Shape): 1/4 turn anti-clockwise
* Shape 3 (Steps): 1/2 turn
* Shape 4 (Triangle): 1/2 turn
* Shape 5 (L-Shape): 1/2 turn
* Shape 6 (Arrow): 1/4 turn clockwise
* Shape 7 (Block Shape): 1/2 turn
* Shape 8 (Backwards L): This is a Reflection (Flip), not a rotation.
* Shape 9 (Triangle): 1/4 turn anti-clockwise
Section 1: Left Worksheet (Pattern Completion)
Task: Complete the pattern by rotating the shape a quarter turn (90 degrees) in the direction of the arrow.
* Row 1: Triangle rotates clockwise → Arrow points Right.
* Row 2: Triangle rotates clockwise → Diamond (Square rotated). *Wait, looking closely at Row 2:* It starts with a triangle pointing up. The arrow is clockwise. The next shape is a diamond? No, that looks like a separate example. Let's look at the empty boxes.
* Row 3 (Heart): The heart is upright. The arrow shows a clockwise quarter turn. A heart rotated 90° clockwise will point to the right.
* Row 4 (Trapezoid): The trapezoid has the long side on the bottom. The arrow shows a counter-clockwise quarter turn. Rotating it 90° left means the long side will be on the right.
* Row 5 (Curved Line/Crescent): The curve opens to the top-left. The arrow is counter-clockwise. Rotating 90° left means the opening will face down-left.
* Row 6 (Triangle): The triangle points down. The arrow is clockwise. Rotating 90° right means the triangle will point left.
* Row 7 (Semi-circle): The flat side is on the left. The arrow is counter-clockwise. Rotating 90° left means the flat side will be on the bottom.
* Row 8 (Pentagon): The pentagon points up. The arrow is clockwise. Rotating 90° right means the point will face right.
*(Note: Since this is a visual pattern task, the "answer" is drawing the shapes described above.)*
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Section 2: Middle Worksheet (Grid Rotation)
Task: Rotate the shaded shape according to the instructions.
Top Part: Quarter Turn Clockwise
1. Triangle: The hypotenuse goes from top-left to bottom-right. After a 90° clockwise turn, the right angle moves from bottom-left to top-left. The new triangle sits in the top-left corner of its bounding box.
2. L-Shape: The vertical part is on the left. After a 90° clockwise turn, the long part becomes horizontal on the top, and the short part hangs down on the right.
3. Rectangle: It is vertical (tall). After a 90° clockwise turn, it becomes horizontal (wide).
Bottom Part: Quarter Turn Anti-Clockwise (Counter-Clockwise)
1. Triangle: The right angle is at the bottom-left. Rotating 90° left moves the right angle to the bottom-right. The hypotenuse faces top-left.
2. L-Shape: The long part is vertical on the left. Rotating 90° left makes the long part horizontal on the bottom, with the short part sticking up on the left.
3. Arrow: Points right. Rotating 90° left makes it point up.
4. Rectangle: It is horizontal (wide). Rotating 90° left makes it vertical (tall).
---
Section 3: Right Worksheet (Matching Rotations)
Task: Match the numbered shapes (1–8) to the correct instruction based on how they were rotated from the original bold shape.
Original Shapes & Matches:
1. Original: Pentagon (pointing up)
* Shape ①: Pointing left. This is a 90° anti-clockwise (or 270° clockwise) turn.
* *Instruction Match:* Look for "1/4 turn anti-clockwise".
2. Original: L-Shape (standing up, foot to right)
* Shape ②: Lying on back, foot up. This is a 90° anti-clockwise turn.
* Shape ⑤: Upside down. This is a 1/2 turn (180°).
* Shape ⑧: Standing up, foot to left. This is a reflection (flip), not a simple rotation in 2D plane unless specified, but usually these tests stick to rotations. Wait, let's look closer. Shape 8 is a mirror image. If only rotations are allowed, this might be a trick or I need to re-evaluate. Let's look at the other L-shapes.
* Actually, let's look at the instructions provided in the key at the bottom:
* 1/2 turn clockwise
* 1/4 turn clockwise
* 1/4 turn anti-clockwise
* 3/4 turn clockwise (which is same as 1/4 anti-clockwise)
Let's re-evaluate the matches based on standard rotations:
* Group 1: Pentagon
* Original: Point Up.
* Shape ①: Point Left. Rotation: 1/4 turn anti-clockwise (or 3/4 clockwise).
* Shape ④: Point Down-Right? No, Shape 4 is a triangle. Let's group by shape type.
Let's solve by matching each numbered item to its rotation description:
* Item ① (Pentagon pointing Left): From Up to Left is 1/4 turn anti-clockwise.
* Item ② (L-Shape lying down): Original L stands tall with foot right. Shape 2 lies on its back with foot up. This is a 1/4 turn anti-clockwise.
* Item ③ (Zig-Zag/Step shape): Original steps go down-right. Shape 3 steps go down-left. This looks like a reflection or a 1/2 turn? Let's trace it. Top block moves from top-left to bottom-right. This is a 1/2 turn.
* Item ④ (Triangle): Original right-angle triangle (hypotenuse top-left to bottom-right). Shape 4 has hypotenuse top-right to bottom-left. This is a 1/2 turn (180°) or reflection. In rotation terms, rotating 180° keeps the slope negative if it started negative? No.
* Let's visualize: Original triangle vertices roughly (0,1), (1,1), (1,0). Rotate 180 -> (0,-1), (-1,-1), (-1,0). The shape flips.
* Actually, simpler view: The right angle is at bottom-right in original. In Shape 4, the right angle is at top-left. This is a 1/2 turn.
* Item ⑤ (L-Shape upside down): Original stands tall. Shape 5 is upside down. This is a 1/2 turn.
* Item ⑥ (Arrow pointing Down-Left?): Original Arrow points Down. Shape 6 points Left. Down to Left is a 1/4 turn clockwise.
* Item ⑦ (Complex Step Shape): Original has a "C" cutout facing right. Shape 7 has the cutout facing left. This is a 1/2 turn.
* Item ⑧ (L-Shape mirrored?): Original foot right. Shape 8 foot left. This is a reflection. However, if we must choose a rotation, a 1/2 turn would make it upside down. A 1/4 turn would make it lie down. Shape 8 is upright. This implies the question might include reflections or "turns" in 3D? Or perhaps I am misidentifying the original.
* *Correction:* Look at the original L-shape again. It is an 'L'. Shape 8 is a backwards 'L'. This is a Flip (Reflection). If the worksheet strictly says "Rotation", there might be an error in my interpretation or the sheet includes flips.
* *Alternative:* Maybe Shape 8 is the result of a 1/4 turn clockwise followed by a flip? Unlikely.
* *Let's look at the remaining Triangle:*
* Item ⑨ (Triangle pointing Right): Original Hypotenuse \ . Shape 9 Hypotenuse / . Right angle at bottom-left. Original right angle at bottom-right. This is a 1/4 turn anti-clockwise?
* Original: Right angle bottom-right.
* Rotate 90° Anti-Clockwise: Right angle moves to bottom-left. Vertical side becomes horizontal bottom. Horizontal side becomes vertical left.
* Shape 9: Right angle is bottom-left. Vertical side is on the left. Horizontal side is on the bottom. Yes. Item 9 is 1/4 turn anti-clockwise.
Let's refine the Answers for the Right Sheet based on the visible numbers 1-8 (and 9 is cut off or part of another set? The image shows 1-8 clearly in boxes, and a 9th triangle on the far right).
Let's map the specific numbered boxes to the likely intended answers:
* Box 1 (Pentagon): Rotated 90° Left. Answer: 1/4 turn anti-clockwise.
* Box 2 (L-Shape): Rotated 90° Left. Answer: 1/4 turn anti-clockwise.
* Box 3 (Steps): Rotated 180°. Answer: 1/2 turn.
* Box 4 (Triangle): Rotated 180°. Answer: 1/2 turn.
* Box 5 (L-Shape): Rotated 180°. Answer: 1/2 turn.
* Box 6 (Arrow): Original points Down. Shape points Left. That is 90° Right (Clockwise). Answer: 1/4 turn clockwise.
* Box 7 (Blocky C-shape): Rotated 180°. Answer: 1/2 turn.
* Box 8 (Backwards L): As noted, this is a reflection. If forced to choose a rotation from standard options, it doesn't fit. However, looking at the layout, sometimes "Rotation" worksheets loosely use "Turn" to include flips in lower grades, OR I am missing a step.
* *Wait*, look at the original L-shape for #8. Is it possible the original was different? No, it's the same L as #2 and #5.
* Let's check 1/4 turn clockwise for L-shape: Original (Up/Foot-Right) -> 90° CW -> (Right/Foot-Down). That would look like an L lying on its face. That is not #8.
* Let's check 3/4 turn clockwise (same as 1/4 ACW): That is #2.
* There is no rotation that turns an L into a backwards L in 2D. It is a reflection. If the student must write a rotation, the question may be flawed, or "Flip" is an allowed answer despite the header "Rotation". Given the "Eco ink saving" label, this is likely a standard primary school sheet. Primary schools often teach Reflections separately. I will flag #8 as a Reflection/Flip.
* Box 9 (Triangle on far right): Right angle bottom-left. Original right angle bottom-right. This is 1/4 turn anti-clockwise.
Summary of Matches for the Right Worksheet:
* 1/4 turn clockwise: Shape 6 (Arrow)
* 1/4 turn anti-clockwise: Shape 1 (Pentagon), Shape 2 (L-Shape), Shape 9 (Triangle)
* 1/2 turn: Shape 3 (Steps), Shape 4 (Triangle), Shape 5 (L-Shape), Shape 7 (Blocky C)
* Reflection (Flip): Shape 8 (Backwards L)
Final Answer:
Here are the solutions to the problems in the image:
Left Worksheet (Drawing Patterns)
* Heart: Draw the heart pointing to the right.
* Trapezoid: Draw the trapezoid with the long parallel side on the right (vertical).
* Curved Line: Draw the curve opening towards the bottom-left.
* Triangle: Draw the triangle pointing to the left.
* Semi-circle: Draw the semi-circle with the flat edge on the bottom.
* Pentagon: Draw the pentagon with the point facing right.
Middle Worksheet (Grid Rotations)
* Top Row (Clockwise):
1. Triangle: Right angle moves to the top-left.
2. L-Shape: Long side is horizontal on top; short side hangs down on the right.
3. Rectangle: Becomes horizontal (wide).
* Bottom Row (Anti-Clockwise):
1. Triangle: Right angle moves to the bottom-right.
2. L-Shape: Long side is horizontal on the bottom; short side sticks up on the left.
3. Arrow: Points up.
4. Rectangle: Becomes vertical (tall).
Right Worksheet (Matching Instructions)
* Shape 1 (Pentagon): 1/4 turn anti-clockwise
* Shape 2 (L-Shape): 1/4 turn anti-clockwise
* Shape 3 (Steps): 1/2 turn
* Shape 4 (Triangle): 1/2 turn
* Shape 5 (L-Shape): 1/2 turn
* Shape 6 (Arrow): 1/4 turn clockwise
* Shape 7 (Block Shape): 1/2 turn
* Shape 8 (Backwards L): This is a Reflection (Flip), not a rotation.
* Shape 9 (Triangle): 1/4 turn anti-clockwise
Parent Tip: Review the logic above to help your child master the concept of printable shapes for rotational symmetry.
