Question

A(2,-5) B(-7,3) C(1,4)
Ecuatia inaltimii din A in triunghiul ABC?

Answer 1

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

$Fie \: h_{A} \: inaltimea \: din \: A=>h_{A} \perp BC$

Panta lui BC :

$m_{BC}=\frac{y_{C}-y_{B}}{x_{C}-x_{B}} = \frac{4 - 3}{4 - ( - 7)} = \frac{ 1}{4 + 7} = \frac{ 1}{11}$

$h_{A}\perp BC=>m_{h_{A}}\times m_{BC}=-1$

$m_{h_{A}} \times \frac{1}{11} = - 1$

$\frac{1}{11} m_{h_{A}}= -1 = > m_{h_{A}} = -\frac{1}{ \frac{1}{11} } = -11$

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

$h_{A}:y - ( - 5) = -11(x - 2)$

$h_{A}:y + 5 = -11x +22$

$h_{A}:y = -11x + 22 - 5$

$h_{A}: y= -11x + 17$