Question

The coordinates of the two points lying on $x+y=4$ and at a unit distance from the straight line $4x+3y=10$ are

• A. $(-3,1)$, $(7,11)$
• B. $(3,1)$, $(-7,11)$
• C. $(3,1)$, $(7,11)$
• D. $(5,3)$, $(-1,2)$

Answer 1

Answer: (B)

$(3,1)$, $(-7,11)$

Let $P(h,4-h)$ be any point on the line $x+y=4$
According to the given condition,

$\left|\frac{4h+3(4-h)-10}{\sqrt{4^2+3^2}}\right|=1$
$\left|\frac{4h+12-3h-10}{5}\right|=1$
$\Rightarrow |h+2|=5\Rightarrow h+2=\pm 5\Rightarrow h=3,-7$
Hence, required points are $(3,1),(-7,11)$