If `G(3,-5,r)` is centroid of triangle ABC where `A(7,-8,1), B(p,q,5) and C(q+1,5p,0)` are vertices of a triangle then values of p,q,r are respectively

Options

A. 6,5,4
B. `-4,5,4`
C. `-3,4,3`
D. `-2,3,2`

Answer

D

Explanation

Key Idea the centroid of a triangle formed with vertices `P(x_(1),y_(1),z_(1)),Q(x_(2),y_(2),z_(2))` and `R(x_(3),y_(3),z_(3))`
are `((x_(1)+x_(2)+x_(3))/(3),(y_(1)+y_(2)+y_(3))/(3),(z_(1)+z_(2)+z_(3))/(3))`
Here, `((7+p+q+1)/(3),(-8+q+5p)/(3),(1+5+0)/(3))=(3,-5,r)`
`implies((8+p+q)/(3),(-8+5p+q)/(3),2)=(3,-5,r)`
`implies(8+p+q)/93)=3,(-8+5p+q)/(3)=-5,2=r`
`implies8+p+q=9-8+5p+q=-15,r=2`
`impliesp+q=1,5p+q=-7,r=2`
`impliesp+q=1,5p+q=-7,r=2`
`impliesp=-2,q=3,r=2`