Question

Dau funda :)) In reperul cartezian xOy se considera A(4,-7) B(2,1) C(-3,-5) . Scrieți ecuația dreptei d care trece prin punctul A si are panta egala cu panta dreptei BC.

Answer 1

$A(4,-7) \\ B(2,1) \\ C(-3,-5)$

$m_{BC}=\frac{y_{C}-y_{B}}{x_{C}-x_{B}} = \frac{ - 5 - 1}{ - 3 - 2} = \frac{ - 6}{ - 5} = \frac{6}{5}$

$m_{BC} = m_{d} = \frac{6}{5}$

Ecuația dreptei d :

$y-y_{A}=m_{d}(x-x_{A})$

$y - ( - 7) = \frac{6}{5} (x - 4)$

$y + 7 = \frac{6}{5} x - \frac{24}{5}$

$- \frac{6}{5} x + y + 7 - \frac{24}{5} = 0$

$- \frac{6}{5} x + y + \frac{11}{5} = 0$