A(0,0),B(4,0),C(6,7),D(0,3)
Mid point of AB
P(0+42,0+02)⇒P(2,0)
Mid point of BC
Q(4+62,0+72)⇒Q(5,72)
Mid point of CD
R(6+02,7+32)⇒R(3,5)
Mid point of DA
S(0+02,3+02)⇒S(0,32)
Equation of line joining PR
y−0=5−03−2(x−2)y−0=5x−105x−y=10........(i)
Equation of QS
y−72=32−720−5(x−5)y−72=25(x−5)5(2y−7)=4(x−5)10y−35=4x−2010y−4x=15......(ii)
Solving (i) and (ii)
⇒x=52,y=52
So the point of intersection is (52,52)