Question

A(-1;0) B(3;2) C(5;4) Determinati ecuatia medianei duse din vf A in triunghiul ABC

Answer 1

$\ Luam M, mijlocul segmentului BC \rightarrow M( \frac{3+5}{2}, \frac{2+4}{2}) \Rightarrow M(4.3) \\ \\ \ Avem A(-1,0), M(4,3) \quad calculam ecuatia dreptei AM (ec. medianei) \\ \\ \left|\begin{array}{ccc}x&y&1\\-1&0&1\\4&3&1\end{array}\right| =0 \Rightarrow 0-3+4y-0-3x+y = 0\Rightarrow -3x+5y-3=0 \\ \\ \Rightarrow 3x-5y+3=0 \ (ecuatia medianei)$