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

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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