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# Using vectors to describe translations

The line AB has been translated 4 units to the right and 2 units upwards. We say that the displacement vector is .

We always write the horizontal displacement at the top of the vector and the vertical displacement at the bottom.

A move downwards or to the left is indicated by a - sign:

The object X has been translated by the vector to give its image, X'.

Question

P' (7, 2) is the image of P (2, 11) after a translation. What vector describes this translation?

Did you get ?

If so - well done.

To work out the horizontal movement after the translation, subtract the x-coordinates for p from p':

7 - 2 = 5

To work out the vertical movement after the translation, subtract the y-coordinates for p from p':

2 - 11 = - 9

The vector that describes the translation is:

If you are not sure, try drawing a sketch and marking the points P and P' on it.

The shape has been translated 5 units to the right and 9 units downwards.

Remember that any move to the left or downwards needs a - sign.

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