Reflection & Rotation
Reflection → “reflection in the line x = 2” (name + mirror-line EQUATION).
Rotation → “rotation, 90° anticlockwise, about (1, 0)” (name + angle + direction + CENTRE). At 180° no direction is needed.
Core mirror lines are vertical (x = k) or horizontal (y = k), including the axes: the y-axis is x = 0, the x-axis is y = 0. Reflecting (3, 1) in x = 2: the point sits 1 right of the mirror → image 1 left: (1, 1).
Rotation tools: 90° about the origin sends (x, y) → (−y, x) anticlockwise, (y, −x) clockwise; 180° sends (x, y) → (−x, −y). Tracing paper is allowed in the exam — use it!
Reflect the point (3, 1) in the line x = 2.
1 unit right of the mirror → 1 unit left: image (1, 1).
Rotate (4, 1) by 180° about the origin.
(x, y) → (−x, −y): image (−4, −1).
Rotate (2, 3) by 90° anticlockwise about the origin.
(x, y) → (−y, x): image (−3, 2).
A triangle maps to a mirror twin across the line y = −1. Describe the transformation FULLY.
“Reflection in the line y = −1” — name AND equation, nothing less.
Q1. Reflect (5, 2) in the line x = 3.
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Q2. Reflect (−2, 4) in the x-axis.
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Q3. Rotate (3, 5) by 180° about the origin.
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Q4. Rotate (4, 2) by 90° clockwise about the origin.
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(2, −4) ✓ A1
Q5. Triangle A maps to triangle B, a mirror twin across the vertical line through 4 on the x-axis. Describe the transformation FULLY.
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- x = k and y = k mixed up: x = k is VERTICAL (all points with that x).
- Rotation described without its centre — or without the direction (except 180°).
- Two transformations named for one mapping: the exam says SINGLE transformation — one name only.
- Reflection in the wrong axis: in the x-axis, y flips; in the y-axis, x flips.
Try this: Set the rotation to 180° with O at the origin. Where does the point (1, 1) end up? Now move O to (1, 1) and rotate again.
Draw-the-image and describe-fully are guaranteed grid questions worth 2–3 marks each. Next: translations get their own algebra — the column vector.