JEE Main 2021 (Online) 4th August Evening ShiftQuestion 1
One side of a square lies along the line $x-3y+1=0$ and its one vertex is $(1,4)$. If $(a,b)$ and $(c,d)$ are its two vertices on the line $x-3y+1=0$, then
$|a-2|+|c-2|+|b-1|+|d-1|$
is equal to $\_\_\_\_\_\_\_\_$ .
Points and Straight Lines
Answer$4$
Solution
The distance from $(1,4)$ to the line is $\sqrt{10}$ (the side), with foot $(2,1)$. The two vertices on the line are $(2,1)$ and $(5,2)$ or $(-1,0)$. The sum is $0+3+0+1=4$ in both cases.