the vertices of a triangle are (0,0) , (3,0) , and (0,4) . its orthocentre is at

let the given vertices of the triangle be A(0,0) , B(3,0) and C(0,4).

since AC and AB are perpendicular. therefore its ortho-centre is at A(0,0).

orthocentre is the intersection point of the altitudes from the vertices to the opposite sides.