Question

1-Determine a equação geral da reta que passa pelos pontos

a) A(3,2) B(2,1)
b) A(0,2) B(6,0)

2- Determine o coeficiente angular da reta que passa pelos pontos

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

3-dados os pontos AeB de uma reta e seu coeficiente angular determine o valor de K nos seguintes casos

a) A(2,3) B(K,3) e m=1/2

bA(K,2) B(-1,3) e m= 1

Answer 1

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

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

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

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

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

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