The three vertices of a parallelogram PQRS are P(3,-1,2), Q(1,2,-4), R(-1,1,2). Then, the coordinates of the fourth vertex is .
A
(-1,-2,8)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
(1, 2,8)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
(1,-2,8)
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
(1,-2,-8)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution
The correct option is C (1,-2,8) Let the coordinates of the fourth vertex S be (x,y,z).
Since, the diagonals of a parallelogram bisect each other.
So,the mid-points of PR and QS will coincide. ∴(3−12,−1+12,2+22)=(1+x2,2+y2,−4+z2)⇒(1,0,2)=(x+12,y+22,z−42)⇒x+12=1,y+22=0andz−42=2⇒x=1,y=−2andz=8