How do the x- and y-coordinates change when a figure is translated right a units and down b units?

First what you must do in pinpoint a single x,y coordinate in your figure.  Say just for the sake of example that one of your points in your figure is (3,4).  This means that the point is 3 units to the right of the origin and 4 units above the origin.  (The origin is point (0,0) if you didn't know.)  So, if you have this point and your problem says to move the point down 4 units and to the right 1 unit (again this is just an example), you need to individually find the new coordinates.

Since your original point was (3,4) and you need to translate it down 4 units, that means you must subtract 4 from the y value.  This will make your point equal (3,0).  Then, the problem asks you to translate the point over to the right one unit.  This will make your point equal (4,0).

Tada!  You found your newly translated coordinate.  If you are working with more than one point, just simply repeat the same steps but be sure to perform these operations on every point!  Hope this helps! :)