Question

Ecuația Medinei AM a triunghiului A B C unde A ( 1,4), B(3,2) , C(4,6)

Answer 1

A (1,4), B(3,2) , C(4,6)
M-este mijlocul vectorului BC.

=> $M( \frac{3+4}{2}, \frac{2+6}{2})$
=> $M( \frac{7}{2},4)$

Acum calculam ecuatia dreptei AM,   A(1,4);   M(7/2,4)

$\left|\begin{array}{ccc}x&y&1\\1&4&1\\ \frac{7}{2} &4&1\end{array}\right| =0 \\ \\ 4x+4+ \frac{7y}{2} -14-4x-y = 0 \\ \frac{5y}{2} -10 = 0 \\ \frac{5y}{2}=10 \\ 5y= 20 \\ y=4$

=> y=4 este ecuatia medianei AM.