Question

Of the three lines $x+\sqrt{3}y=0,x+y=1,x-\sqrt{3}y=0$ two are equations of two altitides of an equilateral triangle. Prove that the centroid of triangle is the point $(0,0)$

Answer 1

The two lines $x+\sqrt{3}y=0$ and $x-\sqrt{3}y=0$ are equally inclined to x-axis. Hence these will be the two altitudes of equilateral triangle which intersect at $(0,0)$. hence the orthocentre is $(0,0)$ which coincides with centroid.