Question

The point(s) on x+y=4 that lie(s) at a unit distance from the line 4x+3y-10=0 is/are:

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

Answer 1

Answer: (B), (D)

The correct options are
B (-7, 11)
D (3, 1)

For the line x+y=4,
Let x=t
$\Rightarrow$ y=4-t
Let P(t, 4-t) be a point which is at a unit distance from the line 4x+3y-10=0
$\Rightarrow \left(\frac{4t+3(4-t)-10}{\sqrt{4^2+3^2}}\right|=1\Rightarrow \left(t+2\right|=5\Rightarrow t+2=\pm 5\Rightarrow t=-7\mathrm{or}3\mathrm{Hence},\mathrm{the}\mathrm{required}\mathrm{points}\mathrm{are}\left(-7,11\right)\mathrm{and}\left(3,1\right).$