Question

Find the distance between lines y= -2x + 4 and y = -2x + 10 round to the nearest hundredth

Answer 1

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:-

`\\ \sf\longmapsto (|c_2-c_1|)/(√(A^2+B^2))`

`\\ \sf\longmapsto (|-10+4|)/(√(2^2+1^2))`

`\\ \sf\longmapsto (|-6|)/(√(5))`

`\\ \sf\longmapsto (6)/(2.2)`

`\\ \sf\longmapsto 2.7`

Answer 2

• 2.68 units

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)