Question

The distance of the point $(1,2)$ from the line $x+y+5=0$ measured along the line parallel to $3x-y=7$ is equal to

• A. $\frac{4}{\sqrt{10}}$
• B. $40$
• C. $\sqrt{40}$
• D. $10\sqrt{2}$

Answer 1

Answer: (C)

$\sqrt{40}$

Distance is measured along a line whose is equal to line $3x-y=7$

So slope of line which passes through $(1,2)$ is 3 and hence equation of line is $3x-y=1$

Now we have two equation
$3x-y=1$ and $x+y=-5$

On solving we get
$x=-1$ and $y=-4$

Now using the distance formula, we have
$=\sqrt{{(1+1)}^2+{(2+4)}^2}$

$=\sqrt{40}$