The distance between two parallel lines 5x - 12y + 2 = 0 and 5x - 12y - 3 = 0 is given by:

Question

Question

Answer 1

Concept:

The distance between two parallel lines ax + by + c₁ = 0 and ax + by + c₂ = 0 is given by the formula: \(\rm d=\dfrac{|c_1-c_2|}{\sqrt{a^2+b^2}}\).

Calculation:

Using the concept above, we have a = 5, b = -12, c₁ = 2 and c₂ = -3.

∴ \(\rm d=\dfrac{|c_1-c_2|}{\sqrt{a^2+b^2}}\)

= \(\rm \dfrac{|2-(-3)|}{\sqrt{5^2+(-12)^2}}\)

= \(\rm \dfrac{|5|}{\sqrt{169}}\)

= \(\dfrac{5}{13}\).