Question

The sum of the abscissa of all the points on the line $x+y=4$ that lie at a unit distance from the line $4x+3y-10=0$ is

• A. $4$
• B. $-4$
• C. $3$
• D. $-3$

Answer 1

Answer: (B)

$-4$

Let $(h,4-h)$ is a point on $x+y=4$ line
So, distance of $(h,4-h)$ from $4x+3y-10=0$ line is
$d=\left|\frac{4h+3(4-h)-10}{5}\right|=1$
$\left|\frac{h+2}{5}\right|=1$
$|h+2|=5$
$h=3,-7$
So, sum of the abscissa of all point on $x+y=4$ which is unit distance from $4x+3y-10=0$
$=3-7$
$=-4$