The equation of the line joining the centroid with the orthocentre of the triangle formed by the points (-2,3),(2,-1),(4,0) is

Step-by-step solution

Let A D and B E are altitudes of the triangle. Equation of A D is given by aligned y-3 & = -1 Slope of B C (x+2) y-3 & = -1 ( 0+1 4-2 ) (x+2) y-3 & =-2(x+2 y-3 & =-2 x-4 2 x+y+1 & =0 aligned Equation of B E is given by aligned & y+1= -1 Slope of A C (x-2) y+1= -1 ( 0-3 4+2 ) (x-2) & y+1=2(x-2) & y+1=2 x-4 & y=2 x-5 aligned Since, orthocentre is the intersecting point of altitudes. On solving Eqs. (i) and (ii), we get orthocentre (1,-3) . Also, centroid of A B C= ( -2+2+4 3 , 3-1+0 3 ) = ( 4 3 , 2 3 ) Equation of li