Transformations and Matrices Sunday, 09 December 2018

Reflections Example A(1, 0), B(4, 0) , C(4, 5) and D(1, 5) are the vertices of a rectangle. Draw the rectangle on a set of axes. Find the image of each point under the transformation defined by the matrix and place them on the same set of axes. What is the transformation? y x 2 4 – 2 – 4 6 – 6 –1 C’ D’ D C –4 –4 5 B’ A’ A B –1 5 The matrix represents a reflection in the y axis.

What transformation is represented by this matrix? Example Given the points A(2, 2) , B(6, 5) and C(6, 2). Draw the image of triangle ABC under the transformation defined by the matrix What transformation is represented by this matrix? 2 y x 2 4 – 2 – 4 6 – 6 2 5 C’ B’ 6 B 2 6 A C Represents a reflection in the line y = x

Rotations Example Plot points A(1, 0) , B(5, 0) and C(5, 3) onto a set of axes and join them up. Find the image of each point under the transformation defined by the matrix What is the transformation? y x 2 4 – 2 – 4 6 – 6 1 C’ B’ 5 C -3 5 A A B The matrix represents a rotation of 90 anticlockwise centre (0, 0).

Enlargements or Stretches Example Plot points A(0, 2) , B(2, 1) , C(3, 2) and D(2, 3) onto a set of axes and join them up. Find the image of each point under the transformation defined by the matrix What is the transformation? y x 2 4 12 10 – 2 6 8 D’ 6 6 A’ C’ 3 9 D B’ 6 A C 6 B 9 Represents an enlargement with scale factor 3, centre (0, 0)

Transformations by matrices (a) Draw triangle ABC with coordinates A(2, 1) , B(4, 1) and C(4, 5). (b) Draw the image of triangle ABC under the transformation defined by the matrix (c) Which transformation is defined by the matrix ?

2. (a) Draw triangle DEF with coordinates D(–4, 2) , E(–3, 5) and F(0, 5). (b) Draw the image of triangle DEF under the transformation defined by the matrix (c) Which transformation is defined by the matrix ?

3. (a) Draw triangle LMN with coordinates L(3, 2) , M(5, 5) and N(6, 1). (b) Draw the image of triangle LMN under the transformation defined by the matrix (c) Which transformation is defined by the matrix ?

4. (a) Draw triangle PQR with coordinates P(1, 0) , Q(4, 0) and R(4, 2). (b) Draw the image of triangle PQR under the transformation defined by the matrix (c) Which transformation is defined by the matrix ?

5. (a) Draw triangle JKL with coordinates J(0, 0) , K(2, 0) and L(2, 1). (b) Draw the image of triangle JKL under the transformation defined by the matrix (c) Which transformation is defined by the matrix ?

(a) The Diagram shows a picture of a unit square with coordinates A, B and C labelled, where A(1, 0) , B(0, 1) and C(1, 1) (b) Draw the image of the unit square under the transformation defined by the matrix (c) Write down the new coordinates of A and B. What relationship do you notice between these coordinates and the matrix? x y 1 2 3 4 5 6 7 A B C