Q. 125.0( 2 Votes )

Find all the points on the line x + y = 4 that lie at a unit distance from the line 4x+3y=10.

Answer :

Given: points lie on the line x + y = 4 , perpendicular distance = 1 units


To find : points on the line x + y = 4


Formula used:


We know that the distance between a point (m,n) and a line ax + by + c = 0 is given by,


D



The equation of the line is 4x + 3y – 10 = 0 and D=1 units


Here m= x and n= 4 - x (from the equation x + y = 4 ),a = 4 , b = 3 , c = -10


D


D



or


or


or


We know that the points lie on the line x + y = 4


y = 4 – 7 = -3 or y=4-(-3) =7


(7,-3) and (-3,7) are the points on the line x + y = 4 that lie at a unit distance from


4x + 3y = 10.


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