The three vertices of a parallelogram ABCD are A(-1,3,4), B(2,-1,3) and C(5,1,2). Find the co-ordinates of its 4th vertex D.

Answer

N/a

Explanation

Let the co-ordinates of D are (x,y,z).
Co-ordinates of mid-point of AC.
`=((-1+5)/(2),(3+1)/(2),(4+2)/(2))=(2,2,3)`
Co-ordinates of mid-point of BD
`=((2+x)/(2),(-1+y)/(2),(3+z)/(2))`
But the diagonals of a parallelogram bisect each other
`(2+x)/(2)=2,(-1+y)/(2)=2,(3+z)/(2)=3`
`implies x=2, y=5, z=3`
`therefore` Co-ordinates of D=(2,5,3).