SOLUTION: Three vertices of a parallelogram have coordinates (-3,1), (1,4), and (4,3). Find the coordinates of the fourth vertex. How many possible answers are there?

There are three possible answers.  

Let's plot those three points:



One possible solution is a point below (4,3) and to the right of (-3,1).
We observe that (4,3) is 3 units right of and 1 unit down from (1,4).
So we locate a point 3 units to the right of and 1 unit down from (-3,1).
So we add 3 to the x coordinate of (-3,1) and subtract 1 from its y-
coordinate and we get the first solution as (0,0,) the origin.


   

A second possible solution is a point to the left of and above (-3,1).
We observe that (1,4) is 3 units left of and 1 unit up from (4,3).
So we locate a point 3 units to the left of and 1 unit up from (-3,1).
So we subtract 3 from the x coordinate of (-3,1) and add 1 to its y-
coordinate and we get one solution as (-6,2,) 




A third possible solution is a point and to the right of (4,3) and above
(1,4).  We observe that (1,4) is 4 units right of and 3 units up from (-3,1).
So we locate a point 4 units to the right of and 3 units up from (4,3).
So we add 4 to the x coordinate of (4,3) and add 3 from its y-
coordinate and we get a third solution as (8,6) 



Edwin