Question

Se considera punctele A(1,2), B(3,-1) si C(1,-2) sa se afle ecuatia inaltimii din A a triunghiului ABC

Answer 1

$\Delta ABC$

$A(1,2),B(3,-1),C(1,-2)$

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

$Fie\:m_{BC} \: panta \: lui \: BC$

$m_{BC}:\frac{y_{C}-y_{B}}{x_{C}-x_{B}}$

$m_{BC}: \frac{ - 2 - ( - 1)}{1 - 3}$

$m_{BC}: \frac{ - 2 + 1}{ - 2}$

$m_{BC}: \frac{ - 1}{ - 2}$

$m_{BC}: \frac{1}{2}$

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

$m_{h_{A}} \times \frac{1}{2} = - 1$

$m_{h_{A}} = - \frac{1}{ \frac{1}{2} }$

$m_{h_{A}} = - 2$

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

$h_{A}:y - 2 = - 2(x - 1)$

$h_{A}:y - 2 = - 2x + 2$

$h_{A}:2x + y - 2 - 2 = 0$

$h_{A}:2x + y - 4 = 0$