In triangle ABC Orthocentre (0,0) And centroid (-2,-2).one of the vertex is (-6,0).Then find remaining verrtices

someone pl answer

Let given vertex be A=(-6,0) and the other vertices be B=(a,b) and C=(c,d).

G=(-2,-2) gives a+c=0 and b+d=-6.

Slope of AB=b/a+6 and slope of AC=d/c+6.

So,eqn. of altitudes perpendicular to AC and AB are

(a+6)x+by=(a+6)c+bd and (c+6)x+dy=(c+6)a+bd

Both these intersect at (0,0) and so,ac+bd+6c=0=ac+bd+6a.

This gives a=c and so,a=c=0 since a+c=0.

So,bd=0b=0 or d=0.If b=0 then d=-6 and viceversa.

Hence the other two vertices are (0,0) and (0,-6).

Simple yaar,Since G is the centroid,

G=(-6+a+c/3,0+b+d/3)=(-2,-2)

a+c-6=-6 and b+d=-6  (or) a+c=0,b+d=-6.