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Question
Write the distance between the lines 4x + 3y − 11 = 0 and 8x + 6y − 15 = 0.
Solution
The distance between the two parallel lines \[ax + by + c_1 = 0 \text { and } ax + by + c_2 = 0\] is
\[\left| \frac{c_1 - c_2}{\sqrt{a^2 + b^2}} \right|\].
The given lines can be written as
4x + 3y − 11 = 0 ... (1)
\[8x + 6y - 15 = 0 \Rightarrow 4x + 3y - \frac{15}{2} = 0\] ... (2)
Let d be the distance between the lines (1) and (2).
\[d = \left| \frac{- 11 - \left( - \frac{15}{2} \right)}{\sqrt{4^2 + 3^2}} \right| = \frac{7}{10}\] units
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