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Topic 5: Matrices and transformations

Transformations in the plane

10 hours

• Understand translations and their representation as column vectors.
• Use basic linear transformations — dilations of the form (x, y) → (kx, my), rotations about the origin and reflection in a line that passes through the origin — and the representations of these transformations by 2 × 2 matrices. 2 interactives
• Apply these transformations to points in the plane and polygons. 1 interactive
• Understand and use composition of linear transformations and the corresponding matrix products. 1 interactive
• Understand and use inverses of linear transformations and the relationship with the matrix inverse. 1 interactive
• Understand and use the relationship between the determinant and the effect of a linear transformation on area. 1 interactive
• Determine geometric results by matrix multiplications, e.g. showing that the combined effect of two reflections in lines through the origin is a rotation. 1 interactive