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