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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 4 over 2.

image: a graph with two lines plotted, the first at 1,1 and 2,4 the second at 5,3 and 6,6

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:

image: a graph with x plotted at two locations, 1,0 and 3,3

The object X has been translated by the vector -2 over -3 to give its image, X'.


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

toggle answer


Did you get 5 over -9 ?

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:5 over -9

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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