In Delta ABC,A(1, 2),B(3, 4),and C lies on th | vedclass

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(A) Let the coordinates of $C$ be $(x, 0)$ since it lies on the $X$-axis.The coordinates of the centroid $G$ of a triangle with vertices $(x_1, y_1)$,

Vedclass · Accepted Answer

$(-4, 0)$

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(A) Let the coordinates of $C$ be $(x, 0)$ since it lies on the $X$-axis.The coordinates of the centroid $G$ of a triangle with vertices $(x_1, y_1)$,$(x_2, y_2)$,and $(x_3, y_3)$ are given by $(\frac{x_1+x_2+x_3}{3}, \frac{y_1+y_2+y_3}{3})$.Substituting the given values: $G = (\frac{1+3+x}{3}, \frac{2+4+0}{3}) = (\frac{4+x}{3}, 2)$.Since the centroid $G$ lies on the $Y$-axis,its $x$-coordinate must be $0$.Therefore,$\frac{4+x}{3} = 0$.$4+x = 0 \implies x = -4$.Thus,the coordinates of $C$ are $(-4, 0)$.

In $\Delta ABC$,$A(1, 2)$,$B(3, 4)$,and $C$ lies on the $X$-axis. If the centroid $G$ of $\Delta ABC$ is on the $Y$-axis,then find the coordinates of $C$.

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