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

Given O (0, 0) is the orthocenter.Let A (h, k) be third vertex,B(−2,3) , and C(5,−1) the other two vertices.Then the slope of the line through A and O is k/ h, while the lines through B and C have the slope−47 . By the property of the orthocenter, these  two lines must be perpendicular, so we have (kh)(−47)=−1⇒kh=74→(1)Also, 5−2+h3+−1+3+k3=7⇒h+k=16.........(2)Which is not satisfied by the points given in (a), (b), or (c)