The orthocenter of the triangle formed by the lines  x y = 0 and x + y = 1 is

The lines by which triangle is formed are x=0,y=0,x+y=1.  Clearly, it is a right triangle. We know that in a right angled triangle, the orthocenter coincides with the vertex at which right angle is formed. Therefore, the orthocenter is (0, 0).