27 exam-style questions on Matrix transformations of points (reflections, stretches, rotations) — topic 3.9 of Geometry and Trigonometry in the IB Mathematics: Applications and Interpretation syllabus — with answers and explanations. Samples below; the full set is free with an account.
The matrix that reflects a point in the x-axis is applied to the point (3, 5). Determine the image.
Answer: (3, −5)
Reflection in the x-axis uses the matrix [[1, 0], [0, −1]], which negates the y-coordinate, mapping (3, 5) to (3, −5).
State the matrix that represents an anticlockwise rotation of 90° about the origin.
Answer: [[0, −1], [1, 0]]
Using [[cosθ, −sinθ], [sinθ, cosθ]] with θ = 90° gives [[0, −1], [1, 0]]; the other option is the clockwise rotation.
The transformation matrix [[2, 0], [0, 3]] is applied to the point (4, −1). Determine the image.
Answer: (8, −3)
This matrix stretches x by factor 2 and y by factor 3, so (4, −1) maps to (2·4, 3·(−1)) = (8, −3).
A transformation has matrix [[−1, 0], [0, 1]]. Determine which single transformation it represents.
Answer: Reflection in the y-axis
This matrix negates the x-coordinate while leaving y unchanged, which is a reflection in the y-axis.
The matrix [[0, 1], [1, 0]] is applied to the point (2, 7). Determine the image.
Answer: (7, 2)
This matrix swaps the coordinates, representing reflection in the line y = x, so (2, 7) maps to (7, 2).
A rotation of 180° about the origin has matrix [[−1, 0], [0, −1]]. Determine the image of the point (−4, 6).
Answer: (4, −6)
A 180° rotation negates both coordinates, so (−4, 6) maps to (4, −6).
That was 6 of 27 Matrix transformations of points (reflections, stretches, rotations) questions.
Practise all 27 freeStateAO1 · 1–2 marks
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DetermineAO2 · 2–6 marks
Obtain the only possible answer — by calculation, from the graph or by reasoning — and show how.
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27 Matrix transformations of points (reflections, stretches, rotations) questions — free with an account. Spaced repetition, streaks and full exam simulations included.
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