SOLUTION: the diagonals of a parallelogram intersect at (1,1). two vertices are located at (-6,4) and (-3,-1). find the coordinates of the other vertices.

Plot the three given points. The black line connects two vertices,
so it is the left side of the parallelogram.  Since the diagonals
intersect at (1,1), and since the diagonals of a parallelogram
bisect each other, the two green lines are half diagonals.



Next we draw a (red) horizontal line from the lower left vertex (-3,-1) to
the right until it is directly underneath (1,1) and then draw a
vertical line from there directly up to the point (1,1):



That required us to go 4 units right and 2 units up. So to get
the rest of the diagonal, we will start at (1,1), and do the
same, that is we go right 4 units and up 2 units from (1,1):



Now we can draw in the rest of that diagonal:



So we see that the upper right vertex of the parallelogram is
the point (5,3):



Now we will draw the top side of the parallelogram from (-6,4) to (5,3).
In black like the left side:



So the figure won't be cluttered we'll erase the red lines:



Next we will use the same method to complete the other diagonal.
We will draw a (red) horizontal line from the upper left vertex (-6,4) to
the right until it is directly above (1,1) and then draw a
vertical line from there directly down to the point (1,1):



That required us to go 7 units right and 3 units down. So to get
the rest of that diagonal, we will start at (1,1), and do the
same, that is we go right 7 units and down 3 units from (1,1):



Now we can draw in the rest of that diagonal:



So we see that the lower right vertex of the parallelogram is
the point (8,-2):



Again, so the figure won't be cluttered we'll erase the red lines:



Now we'll draw in the other two sides of the parallelogram:



And we're done.  The other two vertices are (5,3) and (8,-2).

Edwin