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 If the image of the point \mathrm{ \left ( 2,1 \right ) } with respect to a line mirror be \mathrm{ \left ( 5,2 \right ) }, find the equation of the mirror.

Option: 1

\mathrm{x+3y-12=0}


Option: 2

\mathrm{3x+y=10}


Option: 3

\mathrm{x-3y-10=0}


Option: 4

\mathrm{3x+y=12}


Answers (1)

best_answer

Find the equation of the perpendicular bisector of the line segment joining \mathrm{\left ( 2,1 \right )} and \mathrm{\left ( 5,2 \right )} 
Slope of line \mathrm{P P^{\prime}=\frac{2-1}{5-2}=\frac{1}{3}}
slope of \mathrm{AB=-3}
Now point \mathrm{0\left(\frac{2+5}{2}, \frac{1+2}{2}\right) \text { or }\left(\frac{7}{2}, \frac{3}{2}\right)}

Now equation of line 
\mathrm{ \mathrm{AB}\ is \left(y-\frac{3}{2}\right)=-3\left(x-\frac{7}{2}\right) \\ \\\\\\ \Rightarrow 2 y-3=-6 x+21 \Rightarrow 6 x+2 y=24\ or\ 3 x+y=12}

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Rakesh

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