In analytical geometry, how do you calculate the centroid of a triangle using the midpoint formula?

Question

The only information you have are the co-ordinates of the median AQ: A (1,3) and Q(7,9)

Answer 1

ratio in which the centroid divides the median is 2:1
so x coordinate of the centroid=(7*2+1*1)/3=5
y coordinate=(9*2+1*3)/3=7
so G(5,7)

Answer 2

You know that the centroid is on a median situated at at 2/3 from the vertix and 1/3 from Q
So if you call C the centroid AQ/CQ = 3 So

(7-1)/ (7-x)=3 6= 21-3x x=5

(9-3)(9-y) =3 6= 27-3y y=7 C(5,7)

Answer 3

Raj is right about the ratio, but be careful to get it the right way round.
If A is a vertex of the triangle, the centroid is (5,7); but if Q is a vertex, it's (3,5).