Mathematics - Straight line Question with Solution | TestHub

On plotting the diagram of given data we get,

Let $Q(h,0)$

$\because$$OP$ reflected by $x+y=1$

So, the image of $Q$ lies on $y=\frac{x}{\sqrt{3}}$

$\therefore \frac{x-h}{1}=\frac{y}{1}=\frac{-2(h-1)}{2}$

$\Rightarrow x=1, y=1-h$

Since it lies on $y=\frac{x}{\sqrt{3}}$

$\therefore 1-h=\frac{1}{\sqrt{3}}$

$\Rightarrow h=1-\frac{1}{\sqrt{3}}=\frac{\sqrt{3}-1}{\sqrt{3}}$

On rationalising the numerator we get,

$\Rightarrow h=\frac{\sqrt{3}-1}{\sqrt{3}}\times \frac{\sqrt{3}+1}{\sqrt{3}+1}$

$\Rightarrow h=\frac{2}{3+\sqrt{3}}$