Translation is a transformation in which every point of a shape moves the same distance in the same direction.

If one shape can fit exactly on top of another using rotation, reflection or translation, then the shapes are congruent.

A vector can be used to describe a translation.

A vertex is the point where two or more line segments meet. The plural is vertices.

Displacement is the distance from the starting point when measured in a straight line.

Checking and securing understanding of translations

Maths

Column vectors

Parallel vectors

Addition with vectors

Subtraction with vectors

Multiplication with vectors

Fluency in arithmetic procedures with vectors

Algebraic vector notation

Parallel vectors in algebraic vector notation

The sum and difference with algebraic vector notation

Fluency in arithmetic procedures with algebraic vector notation

Calculating the magnitude of a vector

Dividing vectors into ratios

Geometric proofs with vectors

Advanced problem solving with vectors

In the prior unit, pupils described a translation using column vector notation. Pupils' understanding of vectors is further developed in this unit, with pupils exploring column vector notation and arithmetic procedures.

In this unit, pupil understanding of vectors is deepened with pupils exploring column vector notation and arithmetic procedures.

Vectors

Two lines are parallel if they are straight lines that are always the same (non-zero) distance apart.

The gradient is a measure of how steep a line is. It is calculated by finding the rate of change in the y-direction with respect to the positive x-direction.

A resultant vector is the single vector that produces the same effect as a combination of other vectors.

The additive inverse of a number is a number that, when added to the original number, gives the sum of 0.

A scalar is a quantity that has magnitude but not direction.

Pythagoras’ theorem states that the sum of the squares of the two shorter sides of a right-angled triangle is equal to the square of the hypotenuse.

When three or more points lie on a single straight line, these points are said to be collinear.

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