Question

If $A(0,4,1),B(a,b,c),C(4,5,0),D(2,6,2)$ are the consecutive vertices of a square, then the distance $BD$ is:

• A. $\sqrt{34}$
• B. $6$
• C. $18$
• D. $3\sqrt{2}$

Answer 1

Answer: (D)

$3\sqrt{2}$

Given vertices of square are $A(0,4,1),B(a,b,c),C(4,5,0),D(2,6,2)$.

The diagonals of a square are equal in lengths.
Length of diagonal $BD=$ Length of diagonal $AC$
$BD=\sqrt{(4^2+1^2+1^2)}=3\sqrt{2}$