Translations
A translation is simply a movement of an object from one place to another. You have seen in the introduction that this movement is represented by an arrow, or vector, which shows how far and in what direction the object is to be translated, or moved. You should have noticed that the arrow can be located anywhere. Where the vector arrow is located does not change its length and direction.
This is important to know, when we look at how points move on a graph. Here's a translation vector shown on axes:
This particular example is a translation vector of [6, 4]. Sometimes the vector is written using round brackets, like this: (6, 4). It is represented by the dark vector arrow.
This vector tells you how all points will be moved. They will be moved six units to the right, and 4 units up.
Can you use the vector (6, 4) to predict where the point A (-2, -5) will move to?
A (-2, -5) moves to A' (4, -1).
Point A moved right 6 and up 4.
(-2+6, -5+4) = (4, -1)
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Here's another example. This time we've chosen the translation vector [2, -4], or (2, -4).
This vector, represented again by a dark arrow, is telling you that all points will be translated (moved) right 2 and down 4.
Notice that we put the vector in two places. You could put it wherever you want. It will always show '2 right, 4 down'.
Where would the point (-5, 11) end up if moved according to the translation [2, -4]?
(-5+2, 11-4) becomes (-3, 7)
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Transformations Menu
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