Constructing translations
A translation is a transformation where a figure is moved along a vector so that each vertex and its image move the same distance and are parallel to the vector. The above translation is accurate, and this can be proved by preforming the same translation without the addition of the graph. Suppose you were given figure ABDC, and vector u. The first step you would do is to pick a point, say point B, and construct a line parallel to vector u. Make a line form point B that intersects vector u, lets call this line m. Next use your compass to make an arc that intersects line m and vector. Without adjusting the compass, make another arc from point B so that it intersects line m. Next, using your compass, measure out the length it is from the point where the first arc intersected line m to where it intersected vector u. Without adjusting your compass, put the point where the second arc intersected line m, and make a little dash where the pencil touches the paper. Make a line from point B that goes through this dash, using a straight edge. This is a parallel line to vector u. Next, use your compass to measure to out the length of vector u. Then, without adjusting the compass, put the point on point B and make a dash where the pencil intersects the parallel line. This is point B', or the translated point of B. Do all of the before mentioned steps with the other points, then connect all the points together. This gives you figure A'B'C'D', or the translated ABCD along vector u. What your left with will look exactly like the image above. This proves that the above image is accurate.

Information: Translations