Question

A line coming from point $\left(3,4\right)$ is reflected on a point A of x-axis and it passes through point $\left(1,8\right)$ then coordinate of point A is

• A. $\left(7/3,0\right)$
• B. $\left(5,0\right)$
• C. $\left(29/3,0\right)$
• D. $\left(9/2,0\right)$

Answer 1

The correct option is C $\left(29/3,0\right)$

A line coming from point (3,4) is reflected on a point A of $x$ axis.

It passes through a point $(1,8)$ then coordinate of point A

(Refer to Image)

A line passing through $(3,4)$ reflects on point A.

On reflection, the ray passes through point Q $(1,8)$.

We need to find coordinate of A

Since point A is on the $x$ axis its $y$ co-ordinate is $0$.

Let, coordinates of point A be $(K,O)$

So, we need to find value of $K$. Let, the $x$ axis to be a mirror. Take the image of $(3,4)$ in $x$ axis, i.e. $(3,-4)$

$=\sqrt{(5-1{)}^2+(3+2)}=16+25=41$

As we know that reflected ray when extended back passes through the image of a point on incident ray, i.e. reflected ray passes through $(3,-4)$ and $(1,8)$.

$\therefore$ From two point from eqn of reflected ray= $x-sy-2a=0$

put $y=0$, point of incidence= $(\frac{29}{3},0)$ .