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Vectors for OCR GCSE Maths

This page covers the following topics:

1. Representing vectors
2. Translation vectors

Vectors can be represented diagrammatically. The magnitude of a vector is represented by the length of the line segment between its two points, whereas the direction is represented by an arrow drawn on the line.

Vectors can also be represented as column vectors. These are two numbers, one on top of the other, between big brackets. The top number represents the horizontal component of the vector, whereas the bottom number represents the vertical component of the vector. If the vector is three-dimensional, the column vector will have a third component, which represents the component in the third direction.

Representing vectors

A column vector can be used to represent a translation. The top number represents the number of units moved in the horizontal direction, with the positive direction being the right direction. The bottom number represents the number of units moved in the vertical direction, with the positive direction being upwards.

Translation vectors

1

State the coordinates of the point (9, 4) after undergoing a translation represented by the column vector (โˆ’2 5).

The top number represents the number of units moved in the horizontal direction, with the positive direction being the right direction. The bottom number represents the number of units moved in the vertical direction, with the positive direction being upwards.
9 โˆ’ 2 = 7
4 + 5 = 9

(7, 9)

image coming soon.png

2

Provide a vector that describes the translation shown shown in the image.

The triangle has moved 5 units to the right and 3 units downwards, therefore the column vector is (5 โˆ’3).

(5 โˆ’3)

image coming soon.png

3

Olivia has translated a square on a coordinate axis as shown in the image. Find the column vector that describes the given translation.

The square has moved 4 units to the right and 5 units upwards, therefore the column vector is given by (4 5)

(4 5)

image coming soon.png

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