90° anticlockwise about origin
(x,y)→(−y,x)
🎯 Learning Objectives
- rotate figures about the origin and other centres;
- state centre, angle and direction;
- use coordinate rules for multiples of 90°;
- find a centre of rotation geometrically.
Introduction
This lesson develops Rotations from meaning and patterns before moving to calculations. Look for what the quantities, shapes or symbols represent, then connect that idea to the method.
Key Notes
Read the definitions and key facts below carefully. Each rule is most useful when you can explain why it fits the situation, not simply recall it.
Complete Description
Rotation = centre + angle + direction.
90° clockwise about origin
(x,y)→(y,−x)
180° about origin
(x,y)→(−x,−y)
Finding the Centre
Join two object points to their images. Construct perpendicular bisectors. Their intersection is the centre of rotation.
Practice Questions
- Rotate (3,2) 90° anticlockwise about the origin.
- Rotate (−4,1) 90° clockwise about the origin.
- Rotate (5,−3) 180° about the origin.
- Why is “rotation of 90°” incomplete?
✅ Check Your Work
Show answers and working
- (−2,3).
- (1,4).
- (−5,3).
- It omits the centre and direction.
🧠 Learn It Visually: Rotations
A rotation is a turn about a fixed point called the centre of rotation. Every point travels along a circular arc.
Centre
The one fixed point around which the figure turns.
Angle
State the size of the turn, usually 90°, 180° or 270°.
Direction
Clockwise and anticlockwise give different images unless the angle is 180°.
🎛️ See the Transformation Happen
Select an option and watch the object change. Compare orientation, size and position.
Choose a transformation.
Think Like a Mathematician: Why does direction not matter for a 180° rotation?
🧷 Remember
A complete rotation description includes centre, angle and direction.
⚠️ Common Mistake
Rotating around the origin when the stated centre is elsewhere.
🎯 Exam Tip
Trace from the centre to one vertex, turn that radius, then repeat for every vertex.
Common Mistakes
- Choosing a rule before identifying what the question describes.
- Skipping working or changing notation part-way through a solution.
- Accepting an answer without checking its size, sign or units.
Exam Focus
Show the mathematical relationship you are using, keep notation consistent and give a clear final answer. Use a quick estimate, diagram or inverse operation to check that the result is reasonable.
Summary
- Understand the meaning of each idea before selecting a method.
- Use definitions, properties and notation consistently.
- Show working and check that the final result is sensible.