Question

A ray of light coming from the point (1, 2) is reflected at a point A on the x-axis and then passes through the point (5, 3). The coordinates of the point A are-

• A. $\left( \frac{13}{5},0 \right)$
• B. $\left( \frac{5}{13},0 \right)$
• C. (–7, 0)
• D. None of these

Answer 1

Answer: (A)

$\left( \frac{13}{5},0 \right)$

Answer 2

Let, the coordinates of point A is (a, 0)

Now –m_AB = m_AR

If AR makes an angle q with +ve x-axis, then AB makes

(p – q), therefore

–m_AB = m_AR

_– $\left( \frac{0 - 2}{\alpha - 1} \right)$= $\left( \frac{0 - 3}{\alpha - 5} \right)$

Ž 2(a – 5) = –3(a –1)

Ž a = $\frac{13}{5}$ \ A is $\left( \frac{13}{5},0 \right)$