Question

Two perpendicular lines are intersecting at $(4,3)$. One meeting coordinate axis at $(4,0)$, find the distance between origin and the point of intersection of other line with the cordinate axes.

• A. $4$
• B. $7$
• C. $3$
• D. $5$

Answer 1

Answer: (C)

$3$

Two perpendicular lines are intersecting at $(4,3)$ where one line is meeting at $(4,0)$ with coordinate axis

Hence equation of one line from $(4,3)$ and $(4,0)$

$y=\frac{3}{0}(x-4)$

$x=4$

The equation of perpendicular line to $x=4$ is $y=\lambda$

The perpenduclar line is passing through $(4,3)$

Hence $\lambda =3$

$y=3$

The another perpendicular line meeting at $(0,3)$ with coordinate axis

So distance of $(0,3)$ from origin is

$d=\sqrt{(3-0{)}^2+(0)}$

$d=3$