# Show that 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.

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.

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