What is the distance from the origin to the c | vedclass

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(D) Let the vertices of the triangle be $A(1, 1)$,$B(0, -7)$,and $C(-4, 0)$.The coordinates of the centroid $(G)$ are given by the formula:$G = \left(

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$\sqrt{5}$

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(D) Let the vertices of the triangle be $A(1, 1)$,$B(0, -7)$,and $C(-4, 0)$.The coordinates of the centroid $(G)$ are given by the formula:$G = \left( \frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3} \right)$Substituting the values:$G = \left( \frac{1 + 0 - 4}{3}, \frac{1 - 7 + 0}{3} \right)$$G = \left( \frac{-3}{3}, \frac{-6}{3} \right) = (-1, -2)$The distance of the centroid $(-1, -2)$ from the origin $(0, 0)$ is calculated using the distance formula:$d = \sqrt{(x - 0)^2 + (y - 0)^2}$$d = \sqrt{(-1)^2 + (-2)^2}$$d = \sqrt{1 + 4} = \sqrt{5}$

What is the distance from the origin to the centroid of the triangle formed by the points $(1, 1)$,$(0, -7)$,and $(-4, 0)$?

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