# Translation of a Quadrilateral

A translation is a transformation that moves every point in a figure the same distance in the same direction. This video shows how to translate a quadrilateral point by point.

## Translation of a Quadrilateral

Quadrilateral ABCD whose vertices are located at A 4, 4, B 6 and 5 10ths, 3, C 5, negative 1 and 5 tenths and D, negative 3, 2 is translated a certain distance across the plane to form Quadrilateral ABCD. If Point A prime is at 1 and 5 tenths 2, what are the coordinates of B prime, C prime and D prime? A translation is simply a slide or a move of something. So Quadrilateral ABCD has been translated or moved a certain amount and all the coordinates in a figure must be translated the same amount.

So if we can figure out how Point A was translated then we can determine how all the other points need to be translated. The original Point A was at 4, 4. When it was translated, it was moved to 1 and 5 tenths, 2.

First let’s look at the x value. Originally it was at 4 and now it’s at 1 and 5 tenths. You can see that on the graph. Here’s it at 4. Now, it’s been moved over to the left – it’s been moved over to 1 and 5 tenths and it’s been moved to the left 2 and 5 tenths places.

Now for the y coordinates. Initially it was at 4 and now it’s been moved to 2 so again you can see that on the graph. It was at 4. It moved down to 2 so it was moved down 2 places. We need to apply the same translation to all of the other points. So Point B was originally at 6 and 5 tenths, 3. So the translation of B it will go 6 and 5 tenths to the left 2 and 5 tenths so we subtract 2 and 5 tenths from 6 and 5 tenths – 6 and 5 tenths minus 2 and 5 tenths is 4 and then from 3 it needs to be translated down 2 so we’re subtracting 2. 3 minus 2 is 1. So those are the new coordinates of Point B. Point C was at 5, negative 1 and 5 tenths so the translation of Point C – left 2 and a half places so from 5 we need to subtract 2 and tenths so that would be 2 and 5 tenths and then it was at negative 1 and 5 tenths and we need to move it down 2 places so that would be at negative 3 and 5 tenths and then D finally was at negative 3, 2 so the translation of D. Take our x coordinate, translate it to the left 2 and 5 tenths or subtract 2 and 5 tenths. That’s negative 5 and 5 tenths. And then our translation of our y coordinate is down 2 or subtract 2, 2 minutes 2 is zero. So the new coordinates for B C and D are these and you can use these to graph the rest of the quadrilateral.