Transformations using matrices

A transformation can be represented as a matrix. We can perform translations, reflections, rotations and enlargements by multiplying a transformation matrix M by another matrix P. Matrix M is always a 2x2 matrix and represents the transformation used, while matrix P contains, in each column, the vertices of the figure we want to perform the transformation on.

For example,

The transformation is represented by M, the vertices of the figure are A(1,2); B(0,3) and C(2,-1). The image under the transformation has vertices A'(1,-2); B'(0,-3) and C'(2,1).

This way we can conclude that the transformation is a REFLECTION in the x-axis.

Similarly, we can get rotations, translations and enlargements by always multiplying a transformation matrix by the matrix with the vertices of the figure, and we obtain the image of the figure under the transformation. Then, by looking at the transformation in the graph, we can guess the type of transformation and describe it fully (axis, vector, centre, angle of rotation, etc.).

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PRACTICE FROM THE BOOK: Page 311, exercises 1, 2 and 3.