SOLUTION: 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?

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): You can put this solution on YOUR website!

Starting at (-1,-4) move up 1 and to the right 3.
(-1,-4)+(3,1)=(2,-3)

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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