Pearson Edexcel IAL Mathematics FP1.6.3 Combinations of transformations

Practise combining matrix transformations, including rotations and stretches, to find the single matrix mapping one shape onto another.

Exam points

multiply transformation matrices in the correct order to map a triangle or hexagon onto its image
determine a combined 2x2 matrix from rotations, stretches or repeated transformations

[Maximum number: 4]

\mathbf{A}=\left(\begin{array}{cc} -\frac{\sqrt{3}}{2} & -\frac{1}{2} \\ \frac{1}{2} & -\frac{\sqrt{3}}{2} \end{array}\right)

(a)

Hence determine the smallest positive integer value of n for which $\mathbf{A}^{n}=\mathbf{I}$

The matrix B represents a stretch scale factor 4 parallel to the x-axis.

[ 1 ]

n=12

Cao but can be embedded
ie $A^{12}=I$

B1

(1)

(b)

Write down the matrix B

The transformation represented by matrix A followed by the transformation represented by matrix B is represented by the matrix C

[ 1 ]

$B= \left(\begin{smallmatrix} 4 & 0\\ 0 & 1 \end{smallmatrix}\right)$

B1

(c)

Determine the matrix C

The parallelogram P is transformed onto the parallelogram $P^{\prime}$ by the matrix C

[ 2 ]

$C=BA= \left(\begin{smallmatrix} 4 & 0\\ 0 & 1 \end{smallmatrix}\right) \left(\begin{smallmatrix} -\frac{\sqrt3}{2} & -\frac12\\ \frac12 & -\frac{\sqrt3}{2} \end{smallmatrix}\right)$ $C= \left(\begin{smallmatrix} -2\sqrt3 & -2\\ \frac12 & -\frac{\sqrt3}{2} \end{smallmatrix}\right)$

M1 A1

All question bank results loaded

FP1.6.3 - Combinations of transformations question 1

Question (a)

Question (b)

Question (c)