The vertices of a triangle ABC are A (2,3,1) , B(-2, 2,0), and C(0,1,-1).
What is the magnitude of the line joining mid points of the sides AC and BC ?

Options

A. `(1)/(sqrt(2))` unit
B. 1 unit
C. `(3)/(sqrt(2))` unit
D. 2 unit

Answer

C

Explanation

Mid-point of A and C, `((2+0)/(2), (3+1)/(2), (1-1)/(2)) = (1,2,0) `
Mid-point of B and C, `((-2+0)/(2), (2+1)/(2), (0-1)/(2))`
`=(-1, (3)/(2), (-1)/(2))`
Magnitude `= sqrt((1+1)^(2)+(2-(3)/(2))^(2)+(1/2)^(2))`
`=sqrt(4+(1)/(4)+1/4)=(3)/(sqrt(2))` units