If the centroid of the triangle with vertices | vedclass

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Question

(A) The centroid $(G)$ of a triangle with vertices $(x_1, y_1), (x_2, y_2),$ and $(x_3, y_3)$ is given by the formula: $G = (\frac{x_1 + x_2 + x_3}{3}

Vedclass · Accepted Answer

$a = 2, b = -5$

Vedclass · Answer

(A) The centroid $(G)$ of a triangle with vertices $(x_1, y_1), (x_2, y_2),$ and $(x_3, y_3)$ is given by the formula: $G = (\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3})$.Given vertices are $(-5, 3), (a, -1),$ and $(6, b)$,and the centroid is $(1, -1)$.Equating the $x$-coordinates: $\frac{-5 + a + 6}{3} = 1 \implies a + 1 = 3 \implies a = 2$.Equating the $y$-coordinates: $\frac{3 - 1 + b}{3} = -1 \implies 2 + b = -3 \implies b = -5$.Therefore,the values are $a = 2$ and $b = -5$.

If the centroid of the triangle with vertices $(-5, 3), (a, -1), (6, b)$ is $(1, -1)$,then find the values of $a$ and $b$.

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