If the origin is the centroid of the triangle whose vertices are $A (2, p, - 3), B (q, - 2, 5)$ and $C (- 5, 1, r)$ , then find the values of $p, q$ and $r$

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Solution

The coordinates of the centroid are gain by $\Rightarrow$
$(\frac{2 + 9 - 5}{3}, \frac{P - 2 + 1}{3}, \frac{- 3 + 5 + r}{3}) \equiv (0, 0, 0)$
$\Rightarrow \frac{q - 3}{3} = 0, \frac{p - 1}{3} = 0, \frac{r + 2}{3} = 0$
$\Rightarrow q = 3, p = 1, r = - 2$

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If the origin is the centroid of the triangle whose vertices are A(2,p,−3),B(q,−2,5) and C(−5,1,r), then find the values of p,q and r

The coordinates of the centroid are gain by ⇒(2+9−53,P−2+13,−3+5+r3)≡(0,0,0)⇒q−33=0,p−13=0,r+23=0⇒q=3,p=1,r=−2

If the origin is the centroid of the triangle whose vertices are $A (2, p, - 3), B (q, - 2, 5)$ and $C (- 5, 1, r)$ , then find the values of $p, q$ and $r$

The coordinates of the centroid are gain by $\Rightarrow$
$(\frac{2 + 9 - 5}{3}, \frac{P - 2 + 1}{3}, \frac{- 3 + 5 + r}{3}) \equiv (0, 0, 0)$
$\Rightarrow \frac{q - 3}{3} = 0, \frac{p - 1}{3} = 0, \frac{r + 2}{3} = 0$
$\Rightarrow q = 3, p = 1, r = - 2$