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LearnEdexcel4MA12016 specificationPapers 1H, 2H · Higher tierVectors and transformation geometry

Papers 1H, 2H · Module

Vectors and transformation geometry

4 subtopics≈ 120 min in total

Start the module: Reflections, rotations and translations Open graphing calculator

Reflections, rotations and translations
Translations slide, reflections flip and rotations turn; all three keep a shape exactly the same size. To "describe fully" you must give every detail: the vector, the mirror line, or the centre, angle and direction.
≈ 30 min
Enlargements and combined transformations
An enlargement multiplies every distance from a fixed centre by the scale factor $k$ . If $0<k<1$ the shape shrinks; if $k$ is negative the image is on the opposite side of the centre and upside down. Combine transformations by doing them in order.
≈ 30 min
Column vectors and magnitude
A vector has a size and a direction. Write it as a column $\dbinom xy$ : $x$ across, $y$ up. Add, subtract and scale vectors component by component, and find the length (magnitude) with Pythagoras.
≈ 25 min
Vector geometry
To find a vector between two points, follow any route along known vectors, adding as you go and subtracting when you travel backwards. Two vectors are parallel if one is a multiple of the other; points are collinear if they are joined by parallel vectors sharing a point.
≈ 35 min