Worksheet on geometric rotations with coordinate grid exercises for students to practice rotating shapes.
Two pages of a math worksheet on rotations, showing exercises with triangles on coordinate grids for students to rotate and describe transformations.
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Show Answer Key & Explanations
Step-by-step solution for: ? Rotation Worksheet - Home Learning | KS3 Maths | Beyond
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Show Answer Key & Explanations
Step-by-step solution for: ? Rotation Worksheet - Home Learning | KS3 Maths | Beyond
The image you uploaded contains a worksheet on rotations in geometry. Rotations are transformations where a figure is turned around a fixed point (the center of rotation) by a certain angle in a specified direction (clockwise or counterclockwise). Below, I will explain how to solve the problems step by step.
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The worksheet includes several tasks related to rotations:
1. Describing rotations.
2. Performing rotations of shapes around given points.
3. Identifying the transformation applied to a shape.
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#### Task 1: Describe the single transformation that takes shape A to shape B
- Example: The task shows two shapes, A and B, and asks to describe the transformation.
- Solution:
- Angle of Rotation: Determine the angle by which the shape has been rotated. Common angles are 90°, 180°, or 270°.
- Direction of Rotation: Check if the rotation is clockwise or counterclockwise.
- Center of Rotation: Identify the fixed point around which the rotation occurs. This could be a vertex, the origin, or another point.
- Description: Combine all the information into a single statement.
For example:
- "This is a rotation of 90° counterclockwise about the origin."
#### Task 2: Rotate the triangle 90° clockwise about (0, 0)
- Steps:
1. Identify the vertices of the triangle.
2. Apply the rule for a 90° clockwise rotation about the origin:
\[
(x, y) \rightarrow (y, -x)
\]
3. Plot the new coordinates to draw the rotated triangle.
Example:
- If the original vertices are \( (1, 2) \), \( (3, 4) \), and \( (2, 1) \):
- \( (1, 2) \rightarrow (2, -1) \)
- \( (3, 4) \rightarrow (4, -3) \)
- \( (2, 1) \rightarrow (1, -2) \)
- Draw the new triangle using these coordinates.
#### Task 3: Rotate the triangle 180° about (2, 1)
- Steps:
1. Identify the vertices of the triangle.
2. Apply the rule for a 180° rotation about a point \((h, k)\):
\[
(x, y) \rightarrow (2h - x, 2k - y)
\]
3. Plot the new coordinates to draw the rotated triangle.
Example:
- If the original vertices are \( (1, 2) \), \( (3, 4) \), and \( (2, 1) \):
- \( (1, 2) \rightarrow (2(2) - 1, 2(1) - 2) = (3, 0) \)
- \( (3, 4) \rightarrow (2(2) - 3, 2(1) - 4) = (1, -2) \)
- \( (2, 1) \rightarrow (2(2) - 2, 2(1) - 1) = (2, 1) \)
- Draw the new triangle using these coordinates.
#### Task 4: Describe the single transformation that maps shape A to shape B
- Steps:
1. Compare the positions and orientations of shapes A and B.
2. Identify the angle and direction of rotation.
3. Determine the center of rotation (e.g., a vertex, the origin, or another point).
Example:
- If shape B is a 90° counterclockwise rotation of shape A about the origin, the description would be:
- "This is a rotation of 90° counterclockwise about the origin."
#### Task 5: Rotate the shape 90° counterclockwise about (1, 1)
- Steps:
1. Identify the vertices of the shape.
2. Apply the rule for a 90° counterclockwise rotation about a point \((h, k)\):
\[
(x, y) \rightarrow (h - (y - k), k + (x - h))
\]
3. Plot the new coordinates to draw the rotated shape.
Example:
- If the original vertices are \( (2, 3) \), \( (4, 5) \), and \( (3, 2) \):
- \( (2, 3) \rightarrow (1 - (3 - 1), 1 + (2 - 1)) = (1 - 2, 1 + 1) = (-1, 2) \)
- \( (4, 5) \rightarrow (1 - (5 - 1), 1 + (4 - 1)) = (1 - 4, 1 + 3) = (-3, 4) \)
- \( (3, 2) \rightarrow (1 - (2 - 1), 1 + (3 - 1)) = (1 - 1, 1 + 2) = (0, 3) \)
- Draw the new shape using these coordinates.
#### Task 6: Describe the single transformation that maps shape A to shape B
- Steps:
1. Compare the positions and orientations of shapes A and B.
2. Identify the angle and direction of rotation.
3. Determine the center of rotation.
Example:
- If shape B is a 180° rotation of shape A about the point \((2, 2)\), the description would be:
- "This is a rotation of 180° about the point (2, 2)."
---
1. Identify the Center of Rotation: This is crucial for performing accurate rotations.
2. Use Rotation Rules:
- 90° clockwise about the origin: \((x, y) \rightarrow (y, -x)\)
- 90° counterclockwise about the origin: \((x, y) \rightarrow (-y, x)\)
- 180° about any point \((h, k)\): \((x, y) \rightarrow (2h - x, 2k - y)\)
3. Plot Points Carefully: Ensure that the new coordinates are plotted accurately on the grid.
---
The solutions to the specific tasks depend on the exact shapes and points provided in the worksheet. However, the general approach outlined above can be applied to each problem. If you need solutions for specific tasks, please provide the details of those tasks, and I can work through them step by step.
Boxed Final Answer:
\[
\boxed{\text{Follow the steps above to solve each rotation problem.}}
\]
---
Worksheet Overview
The worksheet includes several tasks related to rotations:
1. Describing rotations.
2. Performing rotations of shapes around given points.
3. Identifying the transformation applied to a shape.
---
Step-by-Step Solutions
#### Task 1: Describe the single transformation that takes shape A to shape B
- Example: The task shows two shapes, A and B, and asks to describe the transformation.
- Solution:
- Angle of Rotation: Determine the angle by which the shape has been rotated. Common angles are 90°, 180°, or 270°.
- Direction of Rotation: Check if the rotation is clockwise or counterclockwise.
- Center of Rotation: Identify the fixed point around which the rotation occurs. This could be a vertex, the origin, or another point.
- Description: Combine all the information into a single statement.
For example:
- "This is a rotation of 90° counterclockwise about the origin."
#### Task 2: Rotate the triangle 90° clockwise about (0, 0)
- Steps:
1. Identify the vertices of the triangle.
2. Apply the rule for a 90° clockwise rotation about the origin:
\[
(x, y) \rightarrow (y, -x)
\]
3. Plot the new coordinates to draw the rotated triangle.
Example:
- If the original vertices are \( (1, 2) \), \( (3, 4) \), and \( (2, 1) \):
- \( (1, 2) \rightarrow (2, -1) \)
- \( (3, 4) \rightarrow (4, -3) \)
- \( (2, 1) \rightarrow (1, -2) \)
- Draw the new triangle using these coordinates.
#### Task 3: Rotate the triangle 180° about (2, 1)
- Steps:
1. Identify the vertices of the triangle.
2. Apply the rule for a 180° rotation about a point \((h, k)\):
\[
(x, y) \rightarrow (2h - x, 2k - y)
\]
3. Plot the new coordinates to draw the rotated triangle.
Example:
- If the original vertices are \( (1, 2) \), \( (3, 4) \), and \( (2, 1) \):
- \( (1, 2) \rightarrow (2(2) - 1, 2(1) - 2) = (3, 0) \)
- \( (3, 4) \rightarrow (2(2) - 3, 2(1) - 4) = (1, -2) \)
- \( (2, 1) \rightarrow (2(2) - 2, 2(1) - 1) = (2, 1) \)
- Draw the new triangle using these coordinates.
#### Task 4: Describe the single transformation that maps shape A to shape B
- Steps:
1. Compare the positions and orientations of shapes A and B.
2. Identify the angle and direction of rotation.
3. Determine the center of rotation (e.g., a vertex, the origin, or another point).
Example:
- If shape B is a 90° counterclockwise rotation of shape A about the origin, the description would be:
- "This is a rotation of 90° counterclockwise about the origin."
#### Task 5: Rotate the shape 90° counterclockwise about (1, 1)
- Steps:
1. Identify the vertices of the shape.
2. Apply the rule for a 90° counterclockwise rotation about a point \((h, k)\):
\[
(x, y) \rightarrow (h - (y - k), k + (x - h))
\]
3. Plot the new coordinates to draw the rotated shape.
Example:
- If the original vertices are \( (2, 3) \), \( (4, 5) \), and \( (3, 2) \):
- \( (2, 3) \rightarrow (1 - (3 - 1), 1 + (2 - 1)) = (1 - 2, 1 + 1) = (-1, 2) \)
- \( (4, 5) \rightarrow (1 - (5 - 1), 1 + (4 - 1)) = (1 - 4, 1 + 3) = (-3, 4) \)
- \( (3, 2) \rightarrow (1 - (2 - 1), 1 + (3 - 1)) = (1 - 1, 1 + 2) = (0, 3) \)
- Draw the new shape using these coordinates.
#### Task 6: Describe the single transformation that maps shape A to shape B
- Steps:
1. Compare the positions and orientations of shapes A and B.
2. Identify the angle and direction of rotation.
3. Determine the center of rotation.
Example:
- If shape B is a 180° rotation of shape A about the point \((2, 2)\), the description would be:
- "This is a rotation of 180° about the point (2, 2)."
---
General Tips
1. Identify the Center of Rotation: This is crucial for performing accurate rotations.
2. Use Rotation Rules:
- 90° clockwise about the origin: \((x, y) \rightarrow (y, -x)\)
- 90° counterclockwise about the origin: \((x, y) \rightarrow (-y, x)\)
- 180° about any point \((h, k)\): \((x, y) \rightarrow (2h - x, 2k - y)\)
3. Plot Points Carefully: Ensure that the new coordinates are plotted accurately on the grid.
---
Final Answer
The solutions to the specific tasks depend on the exact shapes and points provided in the worksheet. However, the general approach outlined above can be applied to each problem. If you need solutions for specific tasks, please provide the details of those tasks, and I can work through them step by step.
Boxed Final Answer:
\[
\boxed{\text{Follow the steps above to solve each rotation problem.}}
\]
Parent Tip: Review the logic above to help your child master the concept of rotations worksheet answers.
