Question

Let $A$, $B$, $C$ be the feet of the perpendicular segments drawn from a point $P(3,4,5)$ on the $xy$, $yz$ and $zx-$ planes, respectively. Find the distance of the points $A$, $B$, $C$ from the point $P$ (in units) respectively.

• A. $5$, $2$, $4$
• B. $3$, $4$, $5$
• C. $5$, $3$, $4$
• D. $3$, $5$, $4$

Answer 1

Answer: (C)

We have, coordinates of $A=(3,4,0)$
Coordinates of $B=(0,4,5)$, Coordinates of $C=(3,0,5)$
Now, $P=(3,4,5)$
$\therefore PA=\sqrt{{\left(3-3\right)}^2+{\left(4-4\right)}^2+{\left(5-0\right)}^2}=5$ units
$PB=\sqrt{{\left(3-0\right)}^2+{\left(4-4\right)}^2+{\left(5-5\right)}^2}=3$ units
$PC=\sqrt{{\left(3-3\right)}^2+{\left(4-0\right)}^2+{\left(5-5\right)}^2}=4$ units