Q. 55.0( 3 Votes )

Find the distance of the point of intersection of the lines 2x + 3y = 21 and 3x – 4y + 11 = 0 from the line 8x + 6y + 5 = 0.

Answer :

Given:


Lines 2x + 3y = 21 and 3x – 4y + 11 = 0


To find:


The distance of the point of intersection of the lines 2x + 3y = 21 and 3x – 4y + 11 = 0 from the line 8x + 6y + 5 = 0.


Concept Used:


Distance of a point from a line.


Explanation:


Solving the lines 2x + 3y = 21 and 3x 4y + 11 = 0 we get:



x = 3, y = 5


So, the point of intersection of 2x + 3y = 21 and 3x 4y + 11 = 0 is (3, 5).


Now, the perpendicular distance d of the line 8x + 6y + 5 = 0 from the point (3, 5) is
d


Hence, distance is .


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