Transformations in the plane
Specialist Mathematics · Unit 2 — Complex numbers, further proof, trigonometry, functions and transformations · Matrices and transformations
Learning objectives (7)
LO-1Apply these transformations to points in the plane and polygons.LO-2Determine geometric results by matrix multiplications, e.g. showing that the combined effect of two reflections in lines through the origin is a rotation.LO-3Understand and use composition of linear transformations and the corresponding matrix products.LO-4Understand and use inverses of linear transformations and the relationship with the matrix inverse.LO-5Understand and use the relationship between the determinant and the effect of a linear transformation on area.LO-6Understand translations and their representation as column vectors.LO-7Use basic linear transformations: dilations of the form (𝑥, 𝑦) → (𝑎𝑥, 𝑏𝑦), rotations about the origin and reflection in a line that passes through the origin, and the representations of these transformations by 2 × 2 matrices. dilation of factor 𝑎 parallel to the 𝑥-axis and factor 𝑏 parallel to the 𝑦-axis: [𝑎 0 0 𝑏] rotation of angle 𝜃 anticlockwise about the origin: [cos(𝜃) − sin(𝜃) sin(𝜃) cos(𝜃)] reflection in the line 𝑦 = 𝑥 tan(𝜃): [cos(2𝜃) sin(2𝜃) sin(2𝜃) − cos(2𝜃)]
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