If (0, 0),(-2, 1),and (5, 2) are the vertices | vedclass

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(D) The vertices of the triangle are $(x_1, y_1) = (0, 0)$,$(x_2, y_2) = (-2, 1)$,and $(x_3, y_3) = (5, 2)$.The centroid $(G)$ is given by $\left(\fra

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$x - 2y + 1 = 0$

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(D) The vertices of the triangle are $(x_1, y_1) = (0, 0)$,$(x_2, y_2) = (-2, 1)$,and $(x_3, y_3) = (5, 2)$.The centroid $(G)$ is given by $\left(\frac{x_1+x_2+x_3}{3}, \frac{y_1+y_2+y_3}{3}\right) = \left(\frac{0-2+5}{3}, \frac{0+1+2}{3}\right) = (1, 1)$.The given line is $x - 2y = 6$,which can be written as $2y = x - 6$ or $y = \frac{1}{2}x - 3$. The slope of this line is $m = \frac{1}{2}$.Since the required line is parallel to $x - 2y = 6$,its slope will also be $m = \frac{1}{2}$.The equation of the line passing through $(1, 1)$ with slope $m = \frac{1}{2}$ is given by $y - y_1 = m(x - x_1)$.$y - 1 = \frac{1}{2}(x - 1)$$2(y - 1) = x - 1$$2y - 2 = x - 1$$x - 2y + 1 = 0$.

If $(0, 0)$,$(-2, 1)$,and $(5, 2)$ are the vertices of a triangle,then the equation of the line passing through the centroid and parallel to the line $x - 2y = 6$ is:

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