Question 20859
Midpoint Coordinates:
L(-2,1)
M(2,3)
N(3,-2)
LET ABC BE THE TRIANGLE WITH COORDINATES OF VERTICES AS A(X1,Y1),B(X2,Y2),C(X3,Y3).LET L,M,N BE THE MIDPOINTS OF AB,BC,CA RESPECTIVELY.AS PER COORDINATE GEOMETRY MIDPOINT'S COORDINATES ARE GIVEN BY THE ARITHMATIC MEAN OF COORINATES OF THE END POINTS..SO..
L={(X1+X2)/2,(Y1+Y2)/2}
HENCE (X1+X2)/2=-2...OR X1+X2=-2*2=-4
X1+X2=-4......(1)
SIMILARLY WE GET FROM M AND N 
X2+X3=4.........(2)
X3+X1=6...........(3)
ADDING ALL 3 EQNS.1,2,3,WE GET
X1+X2+X2+X3+X3+X1=2(X1+X2+X3)=-4+4+6=6
X1+X2+X3=3.......(4)
NOW SUBTRACTING EQNS..1,2,AND 3 FROM THIS ,WE GET
X3=7
X2=-1
X1=-3
SIMILARLY YOU CAN FIND Y1,Y2,Y3 WHICH WILL COMPLETE YOUR REQUIREMENT..