Question 1205432: Three vertices of a parallelogram are shown in the figure below.
Give the coordinates of the fourth vertex.
(4,5)
(1,-4)
(9,-6)
Found 4 solutions by Edwin McCravy, ikleyn, mccravyedwin, AnlytcPhil:
Answer by Edwin McCravy(20055)   (Show Source):
You can put this solution on YOUR website!
(4,5)
(1,-4)
(9,-6)
Plot the points and connect them:
Draw three lines parallel to each side You can get them
perfectly accurate on graph paper by counting the number
of units left, right, up, down, needed to get them exactly
parallel.
The three answers are (-4,6), (6,-15), and (12,3).
The three parallograms are drawn below:
 
Edwin
Answer by ikleyn(52781)  (Show Source):
You can put this solution on YOUR website! .
Three vertices of a parallelogram are shown in the figure below.
Give the coordinates of the fourth vertex.
(4,5)
(1,-4)
(9,-6)
~~~~~~~~~~~~~~~~
With 3 (three) given points as verices of a parallelogram, there are 3 possible options
for the fourth vertex.
The algorithm of finding this 4-th vertex coordinates is as follows:
(1) you take two vertices  = ( , ) and  = ( , )
by an arbitrary way from the given three vertices.
(2) you calculate the coordinates of the middle point between the selected points and
 = ( , ) = ( , )
(3) finally, you calculate the coordinates of the 4-th vertex as
 = ( , ) = ( , ).
That's all.
Answer by mccravyedwin(407)  (Show Source):
Answer by AnlytcPhil(1806)  (Show Source):
You can put this solution on YOUR website!
This is Edwin again under my alias AnlytcPhil. I found some more errors,
due to my "copy & paste, then change something" method. I forgot to change
some stuff. So you'll notice it's different above.
So. I'll just let you count units on your graph paper as shown on here.
There's no use doing any calculations. Just count the units on the graph
to see how many units left, right, up, or down that you have to count to
get from one point to another.
Edwin
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