1. The Impulse-Momentum Equation
LO: Finding the matrix for a given transformation and vice versa

2. The Impulse-Momentum Equation
LO: Finding the matrix for a given transformation and vice versa
The Impulse-Momentum Equation
Recall from FP1 text book p 47:
and a transformation can be defined by a matrix as follows:
The point P
and the image point P’
are connected by
Given a transformation (eg an enlargement), how can we define it by matrix
Or:
Given matrix
what transformation does it describe?

3. The Impulse-Momentum Equation
LO: Finding the matrix for a given transformation and vice versa
Compare both:
What’s happened to map to ?
Answer….
i.e. point (1,0) has been mapped to and point (0,1) has been mapped to

4. The Impulse-Momentum Equation
LO: Finding the matrix for a given transformation and vice versa
The unit square has vertices O (0,0), A (1,0), B (1,1) and C (0,1)
(0,1)
(1,0) C B A x y
Therefore:
given a transformation, look at the coordinates A’ and C’ i.e. the image of points A (1,0) and C (0,1).
Or:
given the matrix, look at what has happened to transform A to A’, and C to C’.

5. The Impulse-Momentum Equation
LO: Finding the matrix for a given transformation and vice versa
The Impulse-Momentum Equation
Example: Find the matrix which describes a stretch in the x direction with scale factor 3: y C’ C
(0,1) x
A (1,0)
A’ (3,0)
Answer:

6. The Impulse-Momentum Equation
LO: Finding the matrix for a given transformation and vice versa
The Impulse-Momentum Equation
Example: what transformation is defined by the matrix: y
C’ (0,4)
Example: Find the matrix which describes a stretch in the x direction with scale factor 3:
Answer:
A stretch in the y direction with scale factor 4: C
(0,1) A’ x
A (1,0)

7. The Impulse-Momentum Equation
LO: Finding the matrix for a given transformation and vice versa
The Impulse-Momentum Equation

8. The Impulse-Momentum Equation
LO: Finding the matrix for a given transformation and vice versa

9. The Impulse-Momentum Equation
LO: Finding the matrix for a given transformation and vice versa
The Impulse-Momentum Equation
The following transformations of the unit square, are the only ones that you will be expected to carry out:
Reflections:
In the x axis
In the y axis
In the line y = x
In the line y = -x
Rotations about the origin:
Through 90⁰
Through 180⁰
Through 270⁰
Note: Rotations are anti-clockwise, unless stated otherwise
Enlargements, centre the origin:
With positive scale factors
With negative scale factors