Question

In the diagram $M,S,N,P$ and $Q$ are points in a Cartesian plane.
Given that $MSN$ is a straight line and $S$ is the midpoint of $PQ$ the coordinates of $Q$ are:

• A. $(14,10)$
• B. $(14,12)$
• C. $(14,4)$
• D. $(12,4)$

Answer 1

The correct option is C $(14,4)$

As $MSN$ is a str.line ${\therefore }^{\prime }{y}^{\prime }$ coordinate of ${}^{\prime }{s}^{\prime }$ is mid Pt. of Pa and Let $Q$ be $(x,y)$ coordinate

$\Rightarrow \frac{y+18}{2}=10\Rightarrow y=4$

As $PS\perp SN$ and $QS\perp SN$ and ${}^{\prime }{S}^{\prime }$ is mid point.

$\Rightarrow PN=QN$

$\Rightarrow \sqrt{(18-14{)}^2+(10-16{)}^2}$

$=\sqrt{(x-18)+(x-10)}$

$\left[\begin{array}{c}\because In△PSNand△SNQ\\ PS=SQ\\ \begin{array}{c}SN=SN\left(common\right)\\ \begin{array}{c}\angle PSN=\angle QSN={90}^0\\ \therefore ByRHS△PSN\simeq △SNR\end{array}\end{array}\end{array}\right]$

$\Rightarrow 4^2+6^2=(x-18{)}^2+6^2\Rightarrow x-18\pm 4\Rightarrow x-14,4$

$Q$ is ahead of $N\Rightarrow x=14$