Question

The image of the point $P(4,-13)$ in the line mirror $5x+y+6=0,$ is

• A. $(1,-14)$
• B. $(6,-15)$
• C. $(-1,-14)$
• D. none of these

Answer 1

Answer: (C)

$(-1,-14)$

Let $Q(x_1,y_1)$ be the image of the point $P(4,-13)$ in the line mirror $5x+y+6=0$.

$\frac{h-p}{a}=\frac{k-q}{b}=\frac{-(a\times p+b\times q+c)}{a^2+b^2}$
Then, the coordinates of $Q$ are given by$\frac{x_1-4}{5}=\frac{y_1+13}{1}=\frac{-2(5\times 4-13+6)}{5^2+1^2}$
$\Rightarrow \frac{x_1-4}{5}=\frac{y_1-13}{1}=-1$
$x_1-4=-5$ and $y_1+13=-1$
Hence, the image of the point $P(4,-13)$ in the line mirror $5x+y+6=0$ is $(-1,-14)$.