# 2 points coordinates such that two lines to be medians in a triangle

I have the point $A(0,-1)$ and the equations of two lines: $d1: x-y+1=0$ and $d2: 2x-y=0$.Also, I know that $B\in d1$ and $C\in d2$.

I have to find the coordinates of B and C such that d1 and d2 to be medians in ABC triangle.

I found the intersection of d1 and d2 point G(1,2)

@ValiRo

You know that your point G(1,2) is the center of gravity of the triangle. Denoting $$B(x_B, y_B)$$ and $$C(x_C,y_C)$$ you must have (using the formula for the center of gravity)

$$(0+x_B+x_C)/3=1$$ and $$(-1+y_B+y_C)/3=2$$.

If you add these two equations to the equations of $$d1$$ and $$d2$$ (obviously stisfied by $$B(x_B, y_B)$$ and $$C(x_C,y_C)$$ respectively) you get a 4 by 4 linear system that you can easily solve. My solution is $$B(0,1)$$ and $$C(3,6)$$.

Cheers.

• Thanks a lot! I totally forgot about the formula for the center of gravity.Thanks again! – Vali RO Jan 11 at 17:51