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)



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 $C(3,6)$.


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

Your Answer

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

Not the answer you're looking for? Browse other questions tagged or ask your own question.