Question

Find the sum of the abscissas of the points lying on the line $x-y=3$, which lies at a unit distance from $4x-3y=12$.

Answer 1

Answer: 6.00

Let the point is $(a,a-3)$
$\Rightarrow \left|\frac{4a-3(a-3)-12}{5}\right|=1$
$\Rightarrow |a-3|=5$
$\Rightarrow a=8,-2$
$\therefore$ sum $=6$