Rotating Shapes
Table Of Contents
🎬 Math Angel Video: How to Rotate a Shape
What is Rotation?
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🛎️ Definition of Rotation in Maths:
A rotation is a transformation that turns a shape around a fixed point without changing its size or shape.
❇️ Key Concepts in Rotation:
Centre of Rotation:
The fixed point the shape turns around.Direction of Rotation:
Either clockwise or anticlockwise.Angle of Rotation:
How far the shape is turned, measured in degrees (e.g., 90°, 180°, 270°).
❇️ Key Idea:
A rotation changes only the position of a shape. It keeps the shape the same size, same angles, only turned around the centre.
How to Rotate Shapes (Method 1: Using Tracing Paper)
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Task:
Rotate shape P by 90° clockwise about point O.
🛎️ Steps to Rotate Using Tracing Paper:
Trace the shape
Place tracing paper over the shape and mark the key points on it carefully.Mark the centre of rotation
Put a clear dot on the tracing paper exactly at point O.Rotate the tracing paper
Turn the tracing paper 90° clockwise, keeping the pin or finger fixed on O.Redraw the shape
Plot the new position of each point, then join them to form the rotated shape.
❇️ Key Idea:
Tracing paper lets you physically rotate the shape, so you can see exactly where every point moves.
How to Rotate Shapes (Method 2: Drawing Auxiliary Lines)
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Task:
Rotate shape P by 90° anticlockwise about point O.
🛎️ Steps to Rotate Using Auxiliary Lines:
Join each vertex to the centre
Draw a straight line from every point on the shape to the centre of rotation O.Rotate each line by the given angle
Turn each line 90° anticlockwise.
Keep the length of the line the same.Mark the new points
After rotating each line, place the new point at the same distance from O as the original point.Draw the rotated shape
Join the new points in the same order to form the rotated shape.
❇️ Key Idea:
By rotating each point around the centre and keeping the distance the same, you create an accurate rotated shape.
How to Describe the Rotation?
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Task:
To describe the rotation from shape P to shape Q, follow these steps:
1. Find the centre of rotation
- Join a point on P to its matching point on Q. Draw the perpendicular bisector of this line.
- Repeat with a second pair of matching points.
- The bisectors meet at (2, 3), this is the centre of rotation.
2. Work out the angle
- Draw a line from the centre of rotation (2, 3) to a point on shape P, and a line from the centre to the matching point on Q.
- Measure the angle between these two lines. In this case, the angle between the two lines is a right angle, so the rotation is 90°.
3. Work out the direction
- Moving from right → up is moving anticlockwise around the centre.
- So the rotation is anticlockwise.
❇️ Final Description:
Shape P is rotated 90° anticlockwise about the point (2, 3) to get shape Q.
🍪 Practice: Test Your Understanding with Rotations
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