Discussion Forum

 If G (3,-5,r)  is the 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...

Answer:

Explanation:

 Key idea . The   centroid  of a triangle formed with vertices P(x₁,y₁,z₁), Q( x₂,y₂,z₂)  and R( x₃,y₃,z₃)  are 

$\left(\frac{x_{1}+x_{2}+x_{3}}{3},\frac{y_{1}+y_{2}+y_{3}}{3},\frac{z_{1}+z_{2}+z_{3}}{3}\right)$

 Here,  $\left(\frac{7+p+q+1}{3},\frac{-8+q+5p}{3},\frac{1+5+0}{3}\right)= (3,-5,r)$

$\Rightarrow$   $\left(\frac{8+p+q}{3},\frac{-8+q+5p}{3},2\right)= (3,-5,r)$

$\Rightarrow$     $\frac{8+p+q}{3}=3,\frac{-8+q+5p}{3}=-5,2= r$

$\Rightarrow$    8-p+q=9, -8+5p+q=-15; r=2

$\Rightarrow$   p+q=1, 5p+q=-7, r=2

$\Rightarrow$    p=-2, q=3, r=2