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Question
Find the value of k for which the lines kx – 5y + 4 = 0 and 5x – 2y + 5 = 0 are perpendicular to each other.
Solution
kx − 5y + 4 = 0
`=>` 5y = kx + 4
`=> y = k/5 x + 4/5`
Slope of this line = `m_1 = k/5`
5x − 2y + 5 = 0
`=>` 2y = 5x + 5
`=> y = 5/2 x + 5/2`
Slope of this line = `m_2 = 5/2`
Since, the lines are perpendicular, m1 × m2 = –1
`=> k/5 xx 5/2 = -1`
`=>` k = –2
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