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)

Answer 2

Let $P(h, 4-h)$ be any point on the line $x+y=4$
According to the given condition,
$\left|\frac{4 h+3(4-h)-10}{5}\right|=1$
$\Rightarrow|h+2|=5$
$\Rightarrow h+2=\pm 5$
$\Rightarrow \quad h=3,-7$
Hence, required points are $(3,1),(-7,11)$.