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

The correct option is A (-1, -14)

Let $Q(a,b)$ be the reflection of $P(4,-13)$ in the line $5x+y+6=0$.
Then the mid-point $R(\frac{a+4}{2},\frac{b-13}{2})$ lies on $5x+y+6=0$.
$\therefore 5\left(\frac{a+4}{2}\right)+\frac{b-13}{2}+6=0\Rightarrow 5a+b+19=0$ ......(i)
Also PQ is perpendicular to 5x+y+6=0.
Therefore $\frac{b+13}{a-4}\times (-\frac{5}{1})=-1\Rightarrow a-5b-69=0$ .....(ii)
Solving (i) and (ii), we get $a=-1,b=-14$.