Question

The reflection of the point (4, –13) in the line $5x + y + 6 = 0$ is

• A. (–1, –14)
• B. (3, 4)
• C. (1, 2)
• D. (–4, 13)

Answer 1

Answer: (A)

(–1, –14)

Answer 2

Let $Q(a,b)$ be the reflection of $P(4, - 13)$ in the line

$5x + y + 6 = 0$. Then the point $R\left( \frac{a + 4}{2},\frac{b - 13}{2} \right)$ lies on

$5x + y + 6 = 0$ .

$\therefore$ $5\left( \frac{a + 4}{2} \right) + \left( \frac{b - 13}{2} \right) + 6 = 0$ ⇒ $5a + b + 19 = 0$ .....(i)

Also PQ is perpendicular to $5x + y + 6 = 0$. Therefore

$\left( \frac{b + 13}{a - 4} \right) \times \left( \frac{- 5}{1} \right)$ ⇒ $a - 5b - 69 = 0$ .....(ii)

Solving (i) and (ii), we get $a = - 1,b = - 14$.