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  4. The reflection of the point (1,1) along the line y = -x is

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Q. The reflection of the point $(1,1) $ along the line $ y = -x$ is

KCETKCET 2012Straight Lines

Solution:

The mid-point of $PQ$ lies on $x + y = 0$
image
$\left(\frac{h+1}{2}\right)+\left(\frac{k+1}{2}\right)=0$
$h+k=- 2 \,\,\,\,\,\dots(i)$
Again, PQ is perpendicular to AB.
$\therefore \left(\frac{k-1}{h-1}\right)\left(-1\right)=-1\,\left(\because m_{1} m_{2} = -1\right)$
$\Rightarrow k-1=h-1$
$\Rightarrow k=h$
Put k = h in Eq. (i), we get
$2h =-2$
$ \Rightarrow h=-1$
$\therefore K=-1$