Rotations — The Pivot Point
Three things define a rotation: Angle · Direction · Centre
🎯 Rotation ID
A rotation needs exactly 3 pieces of information:
🧭 Direction Check
Anti-clockwise = Positive
Mathematical convention (like the number line)
Clockwise = Negative
"Going back in time on a clock"
⚙️ Active Rule
90° Anti-Clockwise
(x, y) → (−y, x) about origin
⚠️ Examiner Trap
TRAP 1 — Students describe rotations with only angle and direction, forgetting the centre. Without a centre, the rotation is undefined. Always state all three!
TRAP 2 — Confusing 90° clockwise with 90° anti-clockwise. Check: does the image land where you expect relative to the centre?
✅ Phase 1 Key
At this stage, the centre is always the origin (0, 0). The transformation rules are your golden tools — memorise them!
Working: Point A → A′
Rule for 90° ACW about origin:
(x, y) → (−y, x)
Identify point A:
A(1, 1)
Swap x and y, then negate the new x:
(1, 1) → (−1, 1)
Image point A′:
A′(-1, 1)
All Vertices — Image Coordinates
Rotation applied:
90° Anti-Clockwise about C(0, 0)
📝 Exam Description (Full Marks Answer)
"A rotation of 90° anti-clockwise about the point (0, 0)."
Mark scheme requires: Angle ✓ · Direction ✓ (unless 180°) · Centre coordinates ✓
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