Question 1135008
The diagonals of a parallelogram intersect at (−1,3). One of the sides of the
parallelogram is bounded by (0,6) and (3,1). 
Graph the parallelogram on your paper and find the coordinates of the remaining
vertices. 
<pre><font size=4><b>plot the given points and draw the side of the parallelogram
{{{drawing(600,2700/7,-7,7,-2,7,grid(1),
graph(600,2700/7,-7,7,-2,7),
circle(-1,3,.1),locate(-2.2,3,"(-1,3)"),
circle(0,6,.1),locate(.2,6,"(0,6)"),
circle(3,1,.1),locate(3.2,1,"(3,1)"),
line(0,6,3,1) )}}}
Draw in the two half-diagonals:
{{{drawing(600,2700/7,-7,7,-2,7,grid(1),
graph(600,2700/7,-7,7,-2,7),
circle(-1,3,.1),locate(-2.2,3,"(-1,3)"),
circle(0,6,.1),locate(.2,6,"(0,6)"),
circle(3,1,.1),locate(3.2,1,"(3,1)"),
line(0,6,3,1),green(line(0,6,-1,3),line(-1,3,3,1)) )}}}
To go from (0,6) to (-1,3), you have to go 
1 unit left and 3 units down. So to get the
complete diagonal, start at (-1,3) and do the
same thing. That is go 1 unit left and 3 
units down, like below and you end up at (-2,0):
{{{drawing(600,2700/7,-7,7,-2,7,grid(1),
graph(600,2700/7,-7,7,-2,7),
circle(-1,3,.1),locate(-2.2,3,"(-1,3)"),
circle(0,6,.1),locate(.2,6,"(0,6)"),
circle(3,1,.1),locate(3.2,1,"(3,1)"),locate(-3.1,.6,"(-2,0)"),
line(0,6,3,1),green(line(0,6,-2,0),line(-1,3,3,1))
)}}}
Similarly to go from (3,1) to (-1,3), you have to go 
4 units left and 2 units up. So to get the
complete diagonal, start at (-1,3) and do the
same thing. That is go 4 units left and 2 
units up, like below and you end up at (-5,5):
{{{drawing(600,2700/7,-7,7,-2,7,grid(1),
graph(600,2700/7,-7,7,-2,7),
circle(-1,3,.1),locate(-2.2,3,"(-1,3)"),
circle(0,6,.1),locate(.2,6,"(0,6)"),locate(-6,5,"(-5,5)"),
circle(3,1,.1),locate(3.2,1,"(3,1)"),locate(-3.1,.6,"(-2,0)"),
line(0,6,3,1),green(line(0,6,-2,0),line(-1,3,3,1),line(-5,5,-1,3))
)}}}
Now you can draw in the complete parallelogram:
{{{drawing(600,2700/7,-7,7,-2,7,grid(1),
graph(600,2700/7,-7,7,-2,7),
circle(-1,3,.1),locate(-2.2,3,"(-1,3)"),
circle(0,6,.1),locate(.2,6,"(0,6)"),locate(-6,5,"(-5,5)"),
circle(3,1,.1),locate(3.2,1,"(3,1)"),locate(-3.5,.6,"(-2,0)"),
line(0,6,3,1),green(line(0,6,-2,0),line(-1,3,3,1),line(-5,5,-1,3)),
line(0,6,-5,5), line(3,1,-2,0), line(-2,0,-5,5)
)}}}
Edwin</pre></font></b>