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Question
Find the distance between the parallel lines
3x − 4y + 5 = 0 and 6x − 8y − 15 = 0
Solution
3x – 4y + 5 = 0 and 6x – 8y – 15 = 0
The equation of the given lines are
3x – 4y + 5 = 0 ......(1)
6x – 8y – 15 = 0
3x – 4y – 1 = 0 ......(2)
The distance between the parallel lines (1) and (2) is
d = `(5 - ( - 15/2))/sqrt(3^2 + (- 4)^2`
= `(5 + 15/2)/sqrt(9 + 16)`
= `(10 + 15)/(2sqrt(25))`
= `25/(2 xx 5)`
= `5/2`
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