The absolute value of the sum of the abscissas of all the points on the line `x+y=4` that lie at a unit distance from the line `4x+3y-10=0` is___________

Answer

4

Explanation

Any point on the line x+y = 4 is (t, 4-4), where `t in R.`
Now, the distance of this point from the line 4x+3y-10=0 is 1. Therefore,
`(|4t +3 (4-t)-10|)/(5) = 1`
or |t+2| = 5
i.e., t = 3 or t = -7
Therefore, the sum of values is -4