Question 746030
"Three vertices of a parallelogram are shown in the figure below. Give the coordinates of the fourth vertex."

(-4,8) Top left
(2,6) top right
(?, ?) bottom left
(5,-3) bottom right


{{{drawing(1120/3,400,-6,8,-5,10,grid(1),
circle(-4,8,.15),circle(2,6,.15),circle(5,-3,.15),
locate(-4+.3,8.3,"(-4,8)"), locate(2.3,6.3,"(2,6)"),locate(5.3,-3+.3,"(5,-3)"),
green(line(-4,8,2,6),line(2,6,5,-3))

 )}}}

Next we draw a horizontal (red) line from (2,6) left until we are directly
below the point (-4,8):

{{{drawing(1120/3,400,-6,8,-5,10,grid(1)
circle(-4,8,.15),circle(2,6,.15),circle(5,-3,.15),
locate(-4+.3,8.3,"(-4,8)"), locate(2.3,6.3,"(2,6)"),locate(5.3,-3+.3,"(5,-3)"),
green(line(-4,8,2,6),line(2,6,5,-3)),red(line(-4,6,2,6))

 )}}}

Next we draw a vertical (red) line up to the point (-4,8):

{{{drawing(1120/3,400,-6,8,-5,10,grid(1)
circle(-4,8,.15),circle(2,6,.15),circle(5,-3,.15),
locate(-4+.3,8.3,"(-4,8)"), locate(2.3,6.3,"(2,6)"),locate(5.3,-3+.3,"(5,-3)"),
green(line(-4,8,2,6),line(2,6,5,-3)),red(line(-4,6,2,6),line(-4,6,-4,8))

 )}}} 

Now observe, by counting blocks, (1) that the horizontal red line goes
6 units left of (2,6), and that (2) the vertical line goes 2 units up
to the point (4,8).

Next, we do the same thing at the lower right point (5,-3).
We draw a red horizontal line 6 uints left of (5,-3) and then
2 unites upward, like this:

{{{drawing(1120/3,400,-6,8,-5,10,grid(1)
circle(-4,8,.15),circle(2,6,.15),circle(5,-3,.15),
locate(-4+.3,8.3,"(-4,8)"), locate(2.3,6.3,"(2,6)"),locate(5.3,-3+.3,"(5,-3)"),
green(line(-4,8,2,6),line(2,6,5,-3)),red(line(-4,6,2,6),line(-4,6,-4,8),
line(5,-3,-1,-3),line(-1,-3,-1,-1)), circle(-1,-1,.15)

 )}}}

By counting blocks we see that that red vertical line ended up at (1,1),
so that's the answer.  Now we can draw in the complete parallelogram:

{{{drawing(1120/3,400,-6,8,-5,10,grid(1)
circle(-4,8,.15),circle(2,6,.15),circle(5,-3,.15),
locate(-4+.3,8.3,"(-4,8)"), locate(2.3,6.3,"(2,6)"),locate(5.3,-3+.3,"(5,-3)"),
green(line(-4,8,2,6),line(2,6,5,-3)),red(line(-4,6,2,6),line(-4,6,-4,8),
line(5,-3,-1,-3),line(-1,-3,-1,-1)), circle(-1,-1,.15),
green(line(-1,-1,-4,8),line(-1,-1,5,-3))

 )}}}

Edwin</pre>