Check first which sides are equal in length
easy to see this using pythagorus theorem.
distance between A and B is sqr root of (7-3)^2 +(2-6)^2 = sqr root 32
distance between B and C is sqr root of (4-7)^2 +(3-2)^2 = sqr root 10
distance between C and A is sqr root of (4-3)^2 + (3-6)^2= sqr root 10
so BC = CA
so the line of symmetry must go through the other side AB
centre of AB is [(7+3)/2, (2+6)/2] = (5,4)
and the line must go through the opposite vertex C
so finding the line through the 2 points (5,4) and (4,3)
y=mx+c
m= (4-3)/5-4) =1
y=x+c
substitute either point (4,3)
gives 3=4+c
c=-1
so equation is y=x-1
Check sum:
substitute the other point (5,4)
4=5-1 yes
so all correct
