Respuesta :

mhanifa

Answer:

  • 2.68 units

Step-by-step explanation:

The distance between the parallel lines ax + by + c₁ = 0 and ax + by + c₂ = 0 is:

  • d = |c₂ – c₁| / √(a² + b²)

Convert the given equations into standard form:

  • y= -2x + 4  ⇒ 2x + y - 4 = 0 ⇒ a = 2, b = 1, c₁ = - 4

and

  • y = -2x + 10 ⇒ 2x + y - 10 = 0 ⇒ a = 2, b = 1, c₂ = - 10

Find the distance:

  • d = (10 - 4) / √(2² + 1²) = 6 / √5 = 2.68 (rounded)

A equation be Ax+By+C=0

Now given lines are.

  • y=2x+4
  • y=-2x+10

Where

  • A=2,B=1,c1=-4,c2=-10

Now

Distance:-

[tex]\\ \sf\longmapsto \dfrac{|c_2-c_1|}{\sqrt{A^2+B^2}}[/tex]

[tex]\\ \sf\longmapsto \dfrac{|-10+4|}{\sqrt{2^2+1^2}}[/tex]

[tex]\\ \sf\longmapsto \dfrac{|-6|}{\sqrt{5}}[/tex]

[tex]\\ \sf\longmapsto \dfrac{6}{2.2}[/tex]

[tex]\\ \sf\longmapsto 2.7[/tex]