Determine the point A(x,y) so that the point A(x,y), B(0,3), C(1,0), D(7,2)
will be the vertices of a parallelogram. The answer is multiple choice, 
a. A(-6,1)
b. A(3,7)
c. A(5,6)
d. A(6,5)

Plot the three given points:

 

Suppose you connect them as above. Then notice
that to go from point C to point B, you have
to travel 1 unit left to (0,0) and then travel 
3 units up to B. Therefore, to go from D to A,
you must do the same. That is, you must travel
left 1 unit left to (6,2), and then travel up 
3 units to A,  So A's x-coordinate is 1 less 
than D's, and A's y-coordinate in 3 more than
D's.  So A is (6,5). That is choice (d).


 
That is the answer, but I though I might add 
that if you connect the three given points 
another way, like this:

 

then there is another possible solution.  
To get it, you notice
that to go from point B to point C, you have
to travel 3 units down to (0,0) and then travel 
1 unit right to B. Therefore, to go from D to A,
you must do the same. That is, you must travel
3 units down to (7,-1), and then travel right 
3 unit to A,  So A's y-coordinate is 3 less 
than D's, and A's x-coordinate in 1 more than
D's.  So A is (8,-1). That was not one of the
choices, but it could have been.




Believe it or not there is still another solution!!! Can you
figure out where it would be? (Hint: you'd need to extend the
graph on the left side.)

Edwin