Question

The centroid of a triangle with vertices (1,2),(-2,4) and (a,b) is (2,2).value of a and b ?

Answer 1

centroid of a triangle = {(x1+x2+x3)/3 , (y1+y2+y3)/3}
hence ;
2 = (1-2+a)/3
6 = -1+a
a = 7
2 = (2+4+b)/3
6 = 6+b
b = 0
hence a = 7 ; b = 0.

Answer 2

The centroid of a triangle is given by[(x1+x2+x3)/3 , (y1+y2+y3)/3]
therefore[(1-2+a)/3 , (2+4+b)/3]  = (2,2)
by equating corresponding coordinates we get 
(a-1)/3 = 2
⇒(a-1) = 6 
⇒a = 6+1 = 7
and(6+b)/3 = 2
6+b = 6 
b = 0
There fore we get (a,b) = (7,0)