Find the value of k for which the lines kx - 5y + 4 = 0 and 5x - 2y + 5 = 0 are perpendicular to each other

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Solution

kx - 5y + 4 = 0

Slope of this line = m1 =

5x - 2y + 5 = 0

Slope of this line = m2 =

Since, the lines are perpendicular, m1m2 = -1

$k over 5 cross times fraction numerator begin display style 5 end style over denominator begin display style 2 end style end fraction equals negative 1 k equals negative 2$

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