If two vertices of a triangle are $A(3,1,4)$ and $B(-4,5,-3)$ and the centroid of the triangle is $G(-1,2,1),$ then the third vertex C of the triangle is
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Logic Tip: The centroid formula works identically for each coordinate component individually. Instead of using full vector notation, you can solve for the $x$, $y$, and $z$ coordinates separately using equations like $x_g = \frac{x_1 + x_2 + x_3}{3}$. For example, solving $-1 = \frac{3 + (-4) + x_3}{3}$ quickly yields $x_3 = -2$.