Q. 44.2( 5 Votes )

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.

Answer :

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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