Question

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

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

Answer 1

The correct option is A $x-2y+5$

Slope of line joining image B$(4,2)$ and object $A(2,6)=-2$
Since, the mirror $L=0$ is perpendicular to the line joining image and object.
So, its slope of line $=\frac{1}{2}$
The object and its image are equidistant from line .
So, the coordinates of the mid-point of $AB$ are $(3,4)$
The equation of line passing through $(3,4)$ with slope $\frac{1}{2}$ is
$y-4=\frac{1}{2}(x-3)$
$\Rightarrow x-2y+5=0$