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Given:

Lines 24x + 7y = 20 and 4x – 3y – 2 = 0

To prove:

The perpendicular let fall from any point on the straight line 2x + 11y – 5 = 0 upon the two straight lines 24x + 7y = 20 and 4x – 3y – 2 = 0 are equal to each other.

Concept Used:

Distance of a point from a line.

Assuming:

P(a, b) be any point on 2x + 11y − 5 = 0

Explanation:

∴ 2a + 11b − 5 = 0

⇒ b ……..(i)

Let d₁ and d₂ be the perpendicular distances from point P
on the lines 24x + 7y = 20 and 4x − 3y − 2 = 0, respectively.

d₁

⇒ d₁

From (1)

⇒ d₁

Similarly,

d₂

⇒ d₂

From (1)

⇒ d₂

∴ d₁ = d₂

Hence proved.