A ray of light coming from the point P(1,2) gets reflected from the point Q on the x-axis …

Question

A ray of light coming from the point $P(1,2)$ gets reflected from the point $Q$ on the $x$-axis and then passes through the point $R(4,3)$. If the point $S(h,k)$ is such that $PQRS$ is a parallelogram, then $h{k}^{2}$ is equal to:

Accepted Answer

$\begin{gathered} {P}^{'}R:y+2=\frac{5}{3}(x-1) \ Q\Rightarrow y=0 \ \frac{6}{5}=a-1\Rightarrow a=\frac{11}{5} \end{gathered}$

Now, $PQRS$ is parallelogram

$\begin{gathered} 	herefore \frac{h+a}{2}=\frac{4+1}{2}\Rightarrow h=5-\frac{11}{5}=\frac{14}{5} \ \frac{2+3}{2}=\frac{k}{2}\Rightarrow K=5 \end{gathered}$

Now $h{k}^{2}=25	imes \frac{14}{5}=14	imes 5=70$

Solutions · 1