Question

Escreva a equação geral da reta determinada pelos pontos: A (-1,4) e B(4,-1) (registre os cálculos) ​

Answer 1

Utilizando o método do determinante, temos:

$\left|\begin{array}{ccc}x_A&y_A&1\\x_B&y_B&1\\x&y&1\end{array}\right| ~=~0\\\\\\\left|\begin{array}{ccc}-1&4&1\\4&-1&1\\x&y&1\end{array}\right| ~=~0\\\\\\\left[~(-1~.~-1~.~1)+(4~.~y~.~1)+(x~.~4~.~1)~\right]-\left[~(1~.~-1~.~x)+(1~.~y~.~-1)+(1~.~4~.~4)~\right]~=~0\\\\\\\left[~(1)+(4y)+(4x)~\right]-\left[~(-x)+(-y)+(16)~\right]~=~0\\\\\\1+4y+4x+x+y-16~=~0\\\\\\5x+5y-15~=~0~~~~Simplificando~por~5\\\\\\\boxed{x+y-3=0}$