SOLUTION: IF A(2,0),B(p,-2),C(-1,1) and D(3,r) are the vertices of a parallelogram ABCD,calculate the value of p and r.

Algebra ->  Graphs -> SOLUTION: IF A(2,0),B(p,-2),C(-1,1) and D(3,r) are the vertices of a parallelogram ABCD,calculate the value of p and r.       Log On


   

Question 1070930: IF A(2,0),B(p,-2),C(-1,1) and D(3,r) are the vertices of a parallelogram ABCD,calculate the value of p and r.

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
The diagonals of a parallelogram bisect each other.
that means that the midpoint of AC is also the midpoint of BD.
Thee coordinates of the midpoint of a segment
are the averages of the corresponding coordinates
of the endpoints of the segment.
The midpoint of AC is ((2+(-1))/2,(0+1)/2) = (1/2,1/2) .
The midpoint of BD is ((p+3)/2,(-2+r)/2) .
So %28p%2B3%29%2F2=1%2F2 <--> p%2B3=1 <--> p=1-3 <--> highlight%28p=-2%29 ,
and
%28-2%2Br%29%2F2=1%2F2 <--> -2%2Br=1 <--> r=1%2B2 <--> highlight%28r=3%29 .