Question 951372: plot the points P (-1,-4) Q ( 1,1) R (4,2) on a coordinate plane. Where should the point S be located that the figure PQRS a parallelogram?
Found 2 solutions by Fombitz, MathLover1:
Answer by Fombitz(32388)   (Show Source):
Answer by MathLover1(20850)  (Show Source):
You can put this solution on YOUR website! P (-1,-4) Q ( 1,1) R (4,2)
if the figure  is a parallelogram, the point S should be located at intersection point of the line parallel to PQ and the line parallel to SR
to find the line parallel to PQ , first find a line PQ:
 ...eq.1
 ...eq.2
-----------------------add
find 
...eq.2
the equation of this line is:
the line  has same slope, so:
 ...since this line passes through R (4,2), we know that 
the equation of this line is:
same way we will find the line SR parallel to QR
the line QR: if Q ( 1,1) R (4,2)
 ...eq.1
...eq.2
-----------------------subtract
 ...eq.2
the equation of this line is:
parallel line is: and passes through P (-1,-4)
intersection of and  is the point S
from the graph, I see the coordinates of the point S are (2,-3)
check if it is true
and 
so, the point  is at ( , )
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