Question

If two vertices of a triangles are $(5,-1)and(-2,3)$ and its orthocentre is at $(0,0)$,then the third vertex is :

Answer 1

Let as assume the third vertex to be (h,k)

A(5,-1) B(-2,3) C(h,k) O(0,0)

(Slope of CO)(Slope of AB)=-1 ...........Since both are perpendicular .......1

(Slope of BC)(Slope of AO)=-1 ...............Since both are perpendicular......2

Solving equations 1 and 2 ,

We get (h,k)=(-4,-7)