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

Question

I have the point and the equations of two lines: and .Also, I know that and .

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)

Answer 1

@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.