Transformation matrices
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Flip to reveal answersHow do you find the image of a point under a 2×2 matrix?
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All 8 Flashcards — Transformation matrices
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Question
How do you find the image of a point under a 2×2 matrix?
Answer
Write the point as a column vector and multiply: matrix on the left, point on the right. (a b; c d)(x; y) = (ax+by; cx+dy).
Question
What is the rotation matrix (anticlockwise about O by θ)?
Answer
(cos θ −sin θ; sin θ cos θ).
Question
What is the enlargement matrix, scale factor k, about O?
Answer
(k 0; 0 k) — multiplies every distance from O by k.
Question
What is the reflection matrix in the line y = (tan θ)x?
Answer
(cos 2θ sin 2θ; sin 2θ −cos 2θ).
Question
Image of (4, 0) under a 90° anticlockwise rotation?
Answer
(0 −1; 1 0)(4; 0) = (0, 4).
Question
Which transformation does (−1 0; 0 −1) represent?
Answer
A rotation of 180° about the origin: (x, y) → (−x, −y).
Question
How do you transform a whole shape by a matrix?
Answer
Transform each vertex (multiply each corner's column vector), then re-join the images.
Question
Which transformation does (1 0; 0 −1) represent?
Answer
A reflection in the x-axis (it flips the sign of y only).
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Full study notes for Transformation matrices
Topic 3.9 hub
Matrix transformations (HL only)
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