Question

4.) Determine a equação geral da reta que passa pelos pontos dados.

a) A(3, 2) e B (2, 1)

b) A(0, 2) e B (6, 0)​

Answer 1

Resposta:

1a) A(3,2) e B(2,1)

\begin{gathered} D= \left[\begin{array}{ccc}x&y&1\\3&2&1\\2&1&1\end{array}\right] \left\begin{array}{ccc}x&y&\\3&2&\\2&1&\end{array}\right =0\\\\ 2x+2y+3-4-x-3y=0\\ x-y-1=0\end{gathered}

b) A(0,2) e B(6,0)

\begin{gathered} D= \left[\begin{array}{ccc}x&y&1\\0&2&1\\6&0&1\end{array}\right] \left\begin{array}{ccc}x&y&\\0&2&\\6&0&\end{array}\right =0\\\\ 2x+6y-12=0\\ \end{gathered}

2a)A(-1,2) B(4,3)

\begin{gathered}D= \left[\begin{array}{ccc}x&y&1\\-1&2&1\\4&3&1\end{array}\right] \left\begin{array}{ccc}x&y&\\-1&2&\\4&3&\end{array}\right =0\\\\\\ 2x+4y-3-8-3x+y=0\\ -x+5y-11=0\\ 5y=x+11\\ \\y= \frac{x+11}{5} \\\\ m= \frac{1}{5}\end{gathered}