Question

if two vertices of aparellelogram are (3,2) and (-1,0) and the diogonals intersect at (2,-5) find the other two vertices of the parellelogram

Answer 1

in a //gm diagonals bisect each other
let ABCD be a //gm
A=(3,2)
B=(-1,0)
C=(x,y)
D=(p,q)
bisecting point D=(2,-5)
D is the midpt of diag AC and BD
using midpt formula,
 for AC
(2,-5)=(3+x/2,2+y/2)
  2=3+x/2               -5=2+y/2
3+x=4                     2+y=-10
x=1                            y=-12
 C=(1,-10)
for BD
(2,-5)=(-1+p/2,0+q/2)
2=-1+p/2             -5=0+q/2
-1+p=4                  q=-10
p=5
D=(5,-10)