Question

If the lines 4x + 3y = 84 and 3x + ky + 7 = 0 are perpendicular to each other. Then the value of k is ______.

Options

• 4

• −4

• `1/4`

• `-1/4`

Answer 1

If the lines 4x + 3y = 84 and 3x + ky + 7 = 0 are perpendicular to each other. Then the value of k is −4.

Explanation:

Given,

1st equation:

⇒ 4x + 3y = 84

⇒ 3y = −4x + 84

⇒ y = `−4/3x + 84/3`

⇒ y = `−4/3x + 28`

Comparing above equation with y = mx + c, we get:

Slope of first equation = `−4/3`

2nd equation:

⇒ 3x + ky + 7 = 0

⇒ ky = −3x − 7

⇒ y = `−3/kx − 7/k`

Slope of second equation = `−3/k`

We know that,

Product of slope of two perpendicular lines = −1

⇒ `−4/3×−3/k = −1`

⇒ `4/k = −1`

⇒ −k = 4

⇒ k = −4