Question

The co-ordinates of the point of reflection of the origin $(0,0)$ in the line $4x-2y-5=0$ is

• A. $(-1,2)$
• B. $(2,-1)$
• C. $(\frac{4}{5},-\frac{2}{5})$
• D. $(2,5)$

Answer 1

The correct option is B $(2,-1)$

Let $(h,k)$ be the point of reflection.
Line joining $(0,0)$ and $(h,k)$ is perpendicular to $4x-2y-5=0$
Product of slopes of these lines is $-1$
$\frac{k}{h}\ast 2=-1=>k=-\frac{h}{2}$
Midpoint of $(0,0)$ and $(h,k)$ i.e, $(\frac{h}{2},\frac{k}{2})$ lies on $4x-2y-5=0$
Therefore $4\frac{h}{2}-2\frac{k}{2}-5=0=>2h-k-5=0$ but $k=-\frac{h}{2}$
$2h+\frac{h}{2}-5=0=>h=2$ and $k=-1$
Point of reflection is $(2,-1)$.