Question

1) Determine a equação geral da reta que passa pelos pontos:
a) A(1, 1) e B(0, 2)
b) A(1, -2) e B(2, -5)
c) A(2, 4) e B(0, 3)
d) A(-2, 5) e B(4, -3)

Answer 1

a)

$\huge\begin{vmatrix}1&1&1\\0&2&1\\x&y&1\end{vmatrix}=0$

$\mathsf{1(2-y)-1(0-x)+1(0-2x)}\\\mathsf{2-y+x-2x=0}\\\mathsf{-x-y+2=0\times(-1)}\\\mathsf{x+y-2=0}$

b)

$\huge\begin{vmatrix}1& - 2&1\\2& - 5&1\\x&y&1\end{vmatrix}=0$

$\mathsf{1(-5-y)+2(2-x)+1(2y+5x)=0)}\\\mathsf{-5-y+4-2x+2y+5x=0}\\\mathsf{3x+y-1=0}$

c)

$\huge\begin{vmatrix}2&4&1\\0&3&1\\x&y&1\end{vmatrix}=0$

$\mathsf{2(3-y)-4(-x)+1(-3x)}\\\mathsf{6-2y+4x-3x=0}\\\mathsf{x-2y+6=0}$

d)

$\huge\begin{vmatrix} - 2&5&1\\4& - 3&1\\x&y&1\end{vmatrix}=0$

$\mathsf{-2(-3-y)-5(4-x)+1(4y+3x)=0}\\\mathsf{6+2y-20+5x+4y+3x=0}\\\mathsf{8x+6y-14=0\div(2)}\\\mathsf{4x+3y-7=0}$