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The displacement from point B to point A is:

So the column matrix representing the displacement is:

e = (-5, -2)T


Coordinate Axes with Vector in the Opposite Direction

When the points are visited in the opposite order, the displacement vector points in the opposite direction. In the column matrix each element is -1 times the old value.

The displacement from A to B is different from the displacement from B to A. Think of displacement as "directions on how to walk from one point to another." So, if you are standing on point A and wish to get to point B, the displacement (5, 2)T says "walk 5 units in the positive X direction, then walk 2 unit in the positive Y direction."

Of course, to get from point B to point A you need different directions: the displacement (-5, -2)T says "walk 5 units in the negative X direction, then walk 2 unit in the negative Y direction," which puts you back on point A.

The displacement from point Start to point Finish :

displacement = (Finish x - Start x , Finish y - Start y)T


Say that point C is   x=4, y=2   and that point D is   x=3, y= 5 .  What column matrix represents the displacement from C to D?

( )T