Question

If $L,M$ are the feet of the perpendiculars from $(2,4,5)$ to $xy-$plane and $yz-$plane respectively, then distance $LM$ (in units) is:

• A. $9\sqrt{2}$
• B. $2\sqrt{2}$
• C. $\sqrt{29}$
• D. $\sqrt{31}$

Answer 1

The correct option is C $\sqrt{29}$

$L=$foot of the perpendicular from $(2,4,5)$ to $xy-$plane $=(2,4,0)$
$M=$ Feet of the perpendicular from $(2,4,5)$ to $yz-$plane $=(0,4,5)$
Applying Distance formula
$LM=\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2+(z_2-z_1{)}^2}$
$\therefore LM=\sqrt{(0-2{)}^2+(4-4{)}^2+(5-0{)}^2}$
$=\sqrt{4+0+25}=\sqrt{29}$ units