Question

The distance between the lines 5x - 12y + 65 = 0 and
10x – 24y - 39 = 0 is​?

Answer 1

Step-by-step explanation:

$Given \: lines \\ 5x - 12y + 65 = 0 \\ 10x - 24y - 39 = 0 \\ \\ Perpendicular \: drawn \: from \: (0 \:, 0) \\ on \: line \: 5x - 12y + 65 = 0 \\ p = \frac{65}{ \sqrt{25 + 144} } = \frac{65}{13} = 5 \: units \\ \\ Perpendicular \: drawn \: from \: (0 \:, 0) \\ on \: line \: 10x - 24y - 39 = 0 \\ p = \frac{ - 39}{ \sqrt{100 + 576} } = \frac{ - 39}{26} = \frac{ - 3}{2} \: units \\ \\ Distance \: between \: two \: lines \: = \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = (5 + \frac{3}{2} ) \: units \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{13}{2} units \\ \\ Hope \: it \: will \: help \: you.$