Question

2)encontre, em cada caso, a forma geral da equação da reta que passa pela pelos pontos dados.
A) (2,2) e(-5,3)
B)(-2,-3)e(4,-1)
C)(10,1)e(1,10)
D)(-3,-4)e(0,1)​

Answer 1

$\large\boxed{\begin{array}{l}\tt a)~\sf\begin{vmatrix}\sf2&\sf2&\sf1\\\sf-5&\sf3&\sf1\\\sf x&\sf y&\sf1\end{vmatrix}=0\\\sf 2\cdot(3-y)-2\cdot(-5-x)+1\cdot(-5y-3x)=0\\\sf 6-2y+10+2x-5y-3x=0\\\sf-x-7y+16=0\cdot(-1)\\\sf x+7y-16=0\end{array}}$

$\large\boxed{\begin{array}{l}\tt b)~\sf\begin{vmatrix}\sf-2&\sf-3&\sf1\\\sf4&\sf-1&\sf1\\\sf x&\sf y&\sf1\end{vmatrix}=0\\\sf-2\cdot(-1-y)+3\cdot(4-x)+1\cdot(4y+x)=0\\\sf2+2y+12-3x+4y+x=0\\\sf-2x+6y+14=0\div(-2)\\\sf x-3y-7=0\end{array}}$

$\large\boxed{\begin{array}{l}\tt c)~\sf\begin{vmatrix}\sf10&\sf1&\sf1\\\sf1&\sf10&\sf1\\\sf x&\sf y&\sf1\end{vmatrix}=0\\\sf 10\cdot(10-y)-1\cdot(1-x)+1\cdot(y-10x)=0\\\sf 100-10y-1+x+y-10x=0\\\sf-9x-9y+99=0\div(-9)\\\sf x+y-11=0\end{array}}$

$\large\boxed{\begin{array}{l}\tt d)~\sf\begin{vmatrix}\sf-3&\sf-4&\sf1\\\sf 0&\sf1&\sf1\\\sf x&\sf y&\sf1\end{vmatrix}=0\\\sf-3\cdot(1-y)+4\cdot(0-x)+1\cdot(0-x)=0\\\sf-3+3y-4x-x=0\\\sf -5x+3y-3=0\cdot(-1)\\\sf 5x-3y+3=0\end{array}}$

Answer 2

Resposta:

Explicação passo a passo:

2)encontre, em cada caso, a forma geral da equação da reta que passa pela pelos pontos dados.

A) (2,2) e(-5,3)

2 2 1 2 2

-5 3 1 -5 3

X y 1 x y

2.3.1+2.1.x+1.(-5).y -[1.3.x+2.1.y+2.(-5).1]=0

6 + 2x - 5y - [ 3x + 2y - 10] = 0

6 + 2x - 5y - 3x - 2y + 10 = 0

- x - 7y + 16 = 0 (-1)

X + 7y - 16 = 0

_____________________

B)(-2,-3)e(4,-1)

-2 -3 1 -2 -3

4 -1 1 4 -1

x y 1 x y

(-2).(-1).1-3.1.x+1.4.y- [1.(-1).x -2.1.y -3.4.1=0

2 - 3x + 4y - [- x - 2y - 12] = 0

2 - 3x + 4y + x + 2y + 12 = 0

- 2x + 6y + 14 = 0 (-1)

2x - 6y - 14 = 0 (:2)

x - 3y - 7 = 0

___________________

_________________

C)(10,1)e(1,10)

10 1 1 10 1

1 10 1 1 10

x y 1 x y

10.10.1+1.1.x+1.1.y - [1.10.x +10.1.y + 1.1.1]=0

100+x+y - [10x + 10y + 1 ] = 0

100+x+y - 10x - 10y - 1 = 0

- 9x - 9y + 99 = 0 (-1)

9x + 9y - 99 = 0 (:9)

x + y - 11 = 0

__________________

D)(-3,-4)e(0,1)​

-3 -4 1 -3 -4

0 1 1 0 1

x y 1 x y

-3.1.1 -4.1.x + 1.0.y - [1.1.x - 3.1.y - 4.0.1]= 0

-3 - 4x + 0 - [ x - 3y - 0] = 0

- 3 - 4x - x+ 3y = 0

- 5x + 3y - 3 = 0 (-1)

5x - 3y + 3 = 0