Question

If $(-2,6)$ is the image of the point $(4,2)$ with respect to the line $L=$ $0$, then $L=$

• A. $6x-4y-7=0$
• B. $2x+3y-5=0$
• C. $3x-2y+5=0$
• D. $3x-2y+10=0$

Answer 1

Answer: (C)

$3x-2y+5=0$

Let points are $A(-2,6)$ & $B(4,2)$

$\therefore$ $L=0$ is $\perp$ to $AB$ & passes through the mid point slope $AB=\frac{-4}{6}=\frac{-2}{3}$

$\therefore$ slope of $L=0=3/2$

passes through $(1,4)$

$\therefore$ required equation is $(y-4)=\frac{3}{2}(x-1)$

$\Rightarrow 2y-8=3x-3$

$\Rightarrow 3x-2y+5=0$ [C]