Question

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

• A. (-1, -14)
• B. (3, 4)
• C. (0, 0)
• D. (1, 2)

Answer 1

The correct option is A

(-1, -14)

Let the reflection point be A (h, k)

Now, the mid point of the line joining (h, k) and (4, -13) will lie on the line $5x+y+6=0$

$\therefore 5\left(\frac{h+4}{2}\right)+\frac{k-13}{2}+6=0$

$\Rightarrow 5h+20+k-13+12=0$

$\Rightarrow 5h+k+19=0...\left(i\right)$

Now, the slope of the line joining points (h, k) and (4, -13) are perpendicular to the line $5x+y+6=0$

Slope of the line $=-5$

Slope of the joining by points (h, k) and (4, -13)

$\frac{k+13}{h-4}$

$\therefore \frac{k+13}{h-4}(-5)=-1$

$\Rightarrow 5k-h+69=0...\left(ii\right)$

Solving (i) and (ii), we get

$h=-1$ and $k=-14$

Hence, the correct answer is option (a).