The Impulse-Momentum Equation

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

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?

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

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’.

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:

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)

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

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

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