Question

if G(3,4) is the centroid of the triangle ABC and A(2,1) B(a,5) C(1,6) find a?​

Answer 1

Step-by-step explanation:

−2,3,2

Given that A(7,−8,1), B(p,q,5) and C(q+1,5p,0) are vertices of a triangle with centroid G(3,−5,r).

We know that, by the centroid formula, the centroid of the triangle ABC is given by : G(g1,g2,g3), where

g1=37+p+q+1,g2=3−8+q+5p,g3=31+5+0.

From the given data,

g1=3,g2=−5,g3=r.

Therefore, we get r=2, 9=8+p+q and −15=−8+q+5p.

That is, r=2, p+q=1 and 5p+q=−7.

So, subtracting the second equation form the third equation, we get 4p=−8. That is, p=−2. Then, the equation p+q=1 gives us −2+q=1. That is, q=3.

So the values of p, q and r are −2, 3 and 2

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