Write the distance between the lines 4x + 3y − 11 = 0 and 8x + 6y − 15 = 0.

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Solution

The distance between the two parallel lines $a x + b y + c_{1} = 0 and a x + b y + c_{2} = 0$ is $|\frac{c_{1} - c_{2}}{\sqrt{a^{2} + b^{2}}}|$ .
The given lines can be written as

4x + 3y − 11 = 0 ... (1)

$8 x + 6 y - 15 = 0 \Rightarrow 4 x + 3 y - \frac{15}{2} = 0$ ... (2)

Let d be the distance between the lines (1) and (2).

$d = |\frac{- 11 - (- \frac{15}{2})}{\sqrt{4^{2} + 3^{2}}}| = \frac{7}{10}$ units

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