A light ray emerging from the point source placed at P(1,3) is reflected at a point Q in t…

Question

A light ray emerging from the point source placed at $P(1,3)$ is reflected at a point $Q$ in the axis of $x$. If the reflected ray passes through the point $R(6,7)$, then the abscissa of $Q$ is:

Accepted Answer

Reflecting $P(1,3)$ in the $x$-axis gives $P'(1,-3)$; the reflected ray is the line $P'R$:
$$\text{slope} = \frac{7-(-3)}{6-1}=2$$

Line: $y+3=2(x-1)$; at $y=0$: $x=\dfrac52$.

Solutions · 1