An Important Question of M.L Aggarwal book of class 10 Based on Equation of a Straight Line Chapter for ICSE BOARD.

If the given straight lines are perpendicular to each other ,Find the value of k.

This is the Question Number 06, Exercise 12.2 of M.L Aggarwal.

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# If the straight lines kx – 5y + 4 = 0 and 4x – 2y + 5 = 0 are perpendicular to each other. Find the value of k.

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Given,

In equation, kx – 5y + 4 = 0

⇒ 5y = kx + 4

y = (k/5) x + 4/5

So, the slope (m

_{1}) = k/5And, in equation 4x – 2y + 5 = 0

⇒ 2y = 4x + 5

y = 2x + 5/2

So, the slope (m

_{2}) = 2As the lines are perpendicular to each other

⇒ m

_{1}x m_{2}= -1k/5 x 2 = -1

k = (-1 x 5)/2

Hence, the value of k = -5/2