If the centroid of the triangle with vertices $(3, a), (b, - 8)$ and $(1, 3)$ is $(3, - 1)$ then find values of $a$ and $b$ .

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Solution

Centroid's coordinates are mean of triangles vertices coordinates
$\Rightarrow 3 = \frac{3 + b + 1}{3} \Rightarrow b + 4 = 9$
$\Rightarrow b = 5$
$\Rightarrow \frac{a - 8 + 3}{3}$
$\Rightarrow a - 5 = - 3$
$\Rightarrow a = 2$ .

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If the centroid of the triangle with vertices (3,a),(b,−8) and (1,3) is (3,−1) then find values of a and b.

Centroid's coordinates are mean of triangles vertices coordinates⇒3=3+b+13⇒b+4=9⇒b=5⇒a−8+33⇒a−5=−3⇒a=2.

If the centroid of the triangle with vertices $(3, a), (b, - 8)$ and $(1, 3)$ is $(3, - 1)$ then find values of $a$ and $b$ .

Centroid's coordinates are mean of triangles vertices coordinates
$\Rightarrow 3 = \frac{3 + b + 1}{3} \Rightarrow b + 4 = 9$
$\Rightarrow b = 5$
$\Rightarrow \frac{a - 8 + 3}{3}$
$\Rightarrow a - 5 = - 3$
$\Rightarrow a = 2$ .