If two vertices of a triangle are (-2,3) and (5,-1), the orthocentre lies at the origin, and the centroid on the line x+y=7, then the third vertex lies at

Given O(0,0) is the orthocentre. Let A(h,k) be the third vertex, and B(-2,3) and C(5,-1) the other two vertices. Then the slope of theline throught A and O is k/h, while the line through B and C has the slope -4/7. By the property of the orthocentre, these two lines must be perependicular. So, we have (hk)(−47)=−1  or kh=74________(i)Also, 5−2+h3+−1+3+k3=7or h+k=16________(ii)Which is not satisfied by the points given in (i),(ii) or (iii).