Question

Wyznacz równanie prostej przechodzącej przez punkty
a) A=(1,1) i B=(2,5).
b) A=(-2,-3) i B=(-4,-5).
c) A=( 1/2 ,2) i B=(-1/2 ,6).

DAJE NAJ
ps.1/2 ulamek :DD

Answer 1

A)
x₁ =1
x₂ = 2
y₁ = 1
y₂ = 5
(x₂ - x₁)(y - y₁) = (y₂ - y₁)(x - x₁)
(2 - 1)(y - 1) = (5 - 1)(x - 1)
y - 1 = 4(x - 1)
y = 4x -4 + 1
y  = 4x - 3
b)
x₁ = - 2
x₂ = - 4
y₁ = - 3
y₂ = - 5
(x₂ - x₁)(y - y₁) = (y₂ - y₁)(x - x₁)
(- 4 + 2)(y + 3) = (- 5 + 3)(x + 2)
- 2(y + 3) = - 2(x + 2)
- 2y - 6 = - 2x - 4
- 2y = - 2x - 4 + 6
- 2y = - 2x + 2
- y = - x + 1
y = x - 1
c)
x₁ = 1/2
x₂ = - 1/2
y₁ = 2
y₂ = 6
(x₂ - x₁)(y - y₁) = (y₂ - y₁)(x - x₁)
(- 1/2 - 1/2)(y - 2) = (6 - 2)(x - 1/2)
- (y - 2) = 4(x - 1/2)
- y + 2 = 4x - 2
-y = 4x - 2 - 2
- y = 4x - 4
y = - 4x + 4