Question

Find the distance between the lines

Y=3x+10
Y=3x-20
AND
Y=3/2x+3/2
Y=3/2x-5

Answer 1

At first we need to know how to find the distance between two parallel lines
The parallel lines which have the same slope
If we have two parallel lines ⇒ y₁ = mx + c₁ and y₂ = mx + c₂
So, the distance between y₁ and y₂ = d =
`\frac{\sqrt{1 + m^(2)}}`
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Part (1):
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The distance between the lines

Y₁ = 3x + 10 and Y₂ = 3x - 20
∴ m = 3 , c₁ = 10 and c₂ = -20
∴ d =
`\frac 10 - (-20){\sqrt{1 + 3^(2)}}= \framebox{9.5}`

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Part (2):
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The distance between the lines

Y₁ = 3/2 x + 3/2 and Y₂ = 3/2 x - 5
∴ m = 3/2 = 1.5 , c₁ = 3/2 = 1.5 and c₂ = -5
∴ d =
`\frac 1.5- (-5){\sqrt{1 + 1.5^(2)}}= \framebox{3.6}`