Question

Se considera triunghiul ABC cu vârfurile A(8,12),B(0,14),C(5,0).
Sa se scrie ecuatiile laturilor triunghiului.

Answer 1

$AB \: : \: \frac{y -y_{A} }{y_{B}-y_{A}} = \frac{x-x_{A}}{x_{B}-x_{A}}$

$AB \: : \: \frac{y - 12}{14 - 12} = \frac{x - 8}{0 - 8}$

$AB \: : \: \frac{y - 12}{2} = \frac{x - 8}{ - 8}$

$AB \: : \: - 8(y - 12) = 2(x - 8)$

$AB \: : \: - 8y + 96 = 2x - 16 \: | \div 2$

$AB \: : \: - 4y + 48 = x - 8$

$AB \: : \: - 4y - x + 48 + 8 = 0$

$AB \: : \: - 4y - x + 56 = 0$

$AC \::\:\frac{y-y_{A}}{y_{C}-y_{A}}=\frac{x-x_{A}}{x_{C}-x_{A}}$

$AC \::\:\frac{y-12}{0-12}=\frac{x-8}{5-8}$

$AC \::\:\frac{y-12}{-12}=\frac{x-8}{ - 3}$

$AC \::\: - 3(y - 12) = - 12(x - 8)$

$AC \::\: - 3y + 36 = - 12x + 96$

$AC \::\: - 3y + 12x + 36 - 96 = 0$

$AC \::\: - 3y + 12x - 60= 0$

$BC\::\:\frac{y-y_{B}}{y_{C}-y_{B}}=\frac{x-x_{B}}{x_{C}-x_{B}}$

$BC\::\:\frac{y-14}{0-14}=\frac{x-0}{5-0}$

$BC\::\:\frac{y-14}{-14}=\frac{x}{5}$

$BC\:: \: 5(y - 14) = - 14x$

$BC\:: \: 5y - 70= - 14x$

$BC\:: \: 5y + 14x - 70= 0$