List the formula for orthocenter,centriod, circumcenter of a triangle in graphical representation

In a triangle,

Centroid(G) divides the orthocentre (H) and circumcentre(S) in the ratio 2:1

Suppose ,

The coordinates of

H be (x1,y1)

G be (X2,y2)

S be (X3,y3)

So,

(x1-x2) : (x2-x3) = 2:1

(y1-y2) : (y2-y3) = 2:1

Solving above two equations , given the two coordinates ,the other one can be found