Question

Escreva a equação geral da reta
a) A(-1 6) e B(2 -3)
b) A(-1,8) B (-5,-1)
c) A(5,0) B (-1,4)
d) A (3,3) B(1,-5)

Answer 1

a) A (-1,6) e B(2,-3)
-----Xa ; Ya--Xb; Yb

M = Yb - Ya
......._______
........Xb - Xa

M = -3 - 6
........_____
........2 - (-1)

M = - 9
.......____
........2 + 1

M = - 9
..... ...__
............3

M = - 3

----------->

(Y - Y1) = M (X - X1)

Y - 6 = - 3 (X + 1)

Y - 6 = - 3X - 3

Y = - 3x - 3 + 6

Y = - 3x + 3


b) A(-1,8) e B(-5,-1)
----Xa ; Ya--Xb ; Yb

M = Yb - Ya
........_______
.........Xb - Xa

M = -1 - 8
........_____
........-5- (-1)

M =...- 9
........____
.........-5 + 1

M = - 9
........____
.........- 4

M = 9
........___
...........4

--------------->

(Y - Y1) = M (X - X1)

(Y - 8) = 9/4 (X - (-1))

(Y - 8) = 9/4 ( X + 1)

4(Y - 8) = 9(X + 1)

4Y - 32 = 9X + 9

4Y - 9X = 9 + 32

4Y - 9X = 41


c) A(5,0) e B(-1,4)
---Xa ; Ya--Xb ; Yb

M = Yb - Ya
........_______
.........Xb - Xa

M = 4 - 0
........_____
........ - 1 - 5

M = 4
.......__
........-6

M = - 4
.........__...(÷2)
...........6

M = - 2
........___
..........3

-------------------->

(Y - Y1) = M (X - X1)

(Y - 0) = -2/3 (X - 5)

3(Y - 0) = - 2(X - 5)

3Y - 0 = -2X + 10

2X + 3Y = 10


d) A(3,3) e B(1,-5)
----Xa ; Ya---Xb ; Yb

M = Yb - Ya
........._______
...........Xb - Xa

M = -5 - 3
........_____
..........1 - 3

M = - 8
........___
.........-2

M = 4

-------------------->

(Y - Y1) = M (X - X1)

(Y - 3) = 4 (X - 3)

(Y - 3) = 4X - 12

Y - 3 = 4X - 12

4X + Y = -12 + 3

4X + Y = - 9