Question

On the portion of the straight line $x+2y=4$ intercepted between the axes, a square is constructed on the side of the line away from the origin. Then the point of intersection of its diagonals has co-ordinates :

• A. $(2,3)$
• B. $(3,2)$
• C. $(3,3)$
• D. none

Answer 1

Answer: (C)

$\tan 45^{\circ }=\left|\frac{m+\frac{1}{2}}{1-\frac{m}{2}}\right|$
$\Rightarrow \pm 1=\frac{2m+1}{2-m}$
$\Rightarrow m=\frac{1}{3},-3$
$\therefore$ Equation of $AC$
$y-2=\frac{1}{3}(x)\Rightarrow x-3y+6=\mathrm{0.....}$(i)
Equation of $BD$
$y=-3(x-4)\Rightarrow 3x+y-12=\mathrm{0......}$(ii)
From (i) \& (ii)
$x=3\&y=3$