1. FP1 Matrices Transformations
BAT use matrix products to represent combinations of transformations

2. WB 11a The points A(1,0), B(0,1) and C(2,0) ate the vertices of a triangle T. The triangle T is rotated 90° anticlockwise around (0,0) and then the image T’ is reflected in the line y = x to obtain the triangle T’’.
a) On separate diagrams, draw T, T’ and T’’
b) i) Find the matrix P such that P(T) = T’
ii) Find the matrix Q such that Q(T’) = T’’
c) By finding a matrix product, find the single matrix that will perform
a 90° anticlockwise rotation followed by a reflection in y = x
(0,1)
(1,0)
(-1,0)
First transformation, the 90° anticlockwise rotation T A B C
Rotated 90° anticlockwise about (0,0) T’ A C B
Reflected in y = x
T’’ A C B
𝑂𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑝𝑎𝑖𝑟:
Replace the coordinates!
𝑁𝑒𝑤 𝑝𝑎𝑖𝑟: 0 −1 1 0
𝑷= 0 −1 1 0

3. WB 11b The points A(1,0), B(0,1) and C(2,0) ate the vertices of a triangle T. The triangle T is rotated 90° anticlockwise around (0,0) and then the image T’ is reflected in the line y = x to obtain the triangle T’’.
a) On separate diagrams, draw T, T’ and T’’
b) i) Find the matrix P such that P(T) = T’
ii) Find the matrix Q such that Q(T’) = T’’
c) By finding a matrix product, find the single matrix that will perform
a 90° anticlockwise rotation followed by a reflection in y = x
(0,1)
(1,0)
2nd transformation, the reflection
in y = x (remember use the standard starting coordinates) T A B C
Rotated 90° anticlockwise about (0,0) T’ A C B
Reflected in y = x
T’’ A C B
𝑂𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑝𝑎𝑖𝑟:
Replace the coordinates!
𝑁𝑒𝑤 𝑝𝑎𝑖𝑟:
𝑷= 0 −1 1 0 𝑸=

4. Rotated 90° anticlockwise about (0,0)
WB 11c The points A(1,0), B(0,1) and C(2,0) ate the vertices of a triangle T. The triangle T is rotated 90° anticlockwise around (0,0) and then the image T’ is reflected in the line y = x to obtain the triangle T’’.
a) On separate diagrams, draw T, T’ and T’’
b) i) Find the matrix P such that P(T) = T’
ii) Find the matrix Q such that Q(T’) = T’’
c) By finding a matrix product, find the single matrix that will perform
a 90° anticlockwise rotation followed by a reflection in y = x T A B C
Rotated 90° anticlockwise about (0,0) T’ A C B
Reflected in y = x
T’’ A C B
𝑷= 0 −1 1 0 𝑸=
It is important to note that P acts first, and then Q acts on P
This is written as …
𝑸𝑷= −1 1 0
𝑸𝑷= −1
Consider how the original coordinates have moved
This is the same as a reflection in the x-axis!

5. This is a 90° rotation clockwise around (0,0)
WB The following matrices represent three different transformations:
𝑷= 𝑸= 𝑹= 3 7 −1 −2
Find the matrix representing the transformation represented by R, followed by Q, followed by P and give a geometrical interpretation of this transformation.
Ensure you get the order correct! R acts first, is acted on by Q which is then acted on by P
PQR = (PQ)R
PQ = =
(PQ)R = −1 −2 =
0 1 −1 0
This is a 90° rotation clockwise around (0,0)
(0,1)
(1,0)
(1,0)
(0,-1)

6. END