Question

The point on the line $x+y=4$ which lies at a unit distance from the line $4x+3y=10$ are

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

Answer 1

The correct option is A $(3,1),(-7,11)$

Let the point $(h,k)$ lie on the line $x+y=4$
then $h+k=4$ ....(i)

and $1=\pm \frac{4h+3k-10}{\sqrt{4^2+3^2}}\Rightarrow 4h+3k=15$ .....(ii)

$4h+5k=5$ .....(iii)

On solving Eqs $\left(i\right)$ and $\left(ii\right)$ and Eqs $\left(i\right)$ and $(iii$, we get the required points $(3,1)$ and $(-7,11)$