Question

The coordinates 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 the image of the point $O(0,0)$ is

$p(h,k)$

$4x-2y-5=0-\left(i\right)$

Equation of $OP$ is

$y-0=\frac{-1}{2}(x-0)$

$\Rightarrow x=-2y-\left(ii\right)$

Using $\left(ii\right)$ in $\left(i\right)$

$4(-2y)-2y-5=0$

$\Rightarrow -10y=5$

$\Rightarrow y=\frac{-1}{2}$

$\therefore x=-2\left(\frac{-1}{2}\right)=1$

Hence, $\alpha (1,\frac{-1}{2})$

$\therefore \frac{\lambda +0}{2}=1,\frac{k+0}{2}=\frac{-1}{2}$

$\therefore \lambda =0,k=-1$

Hence, Image is $(2,-1)$