Two vertices of ΔАBC are A(–1, 4) and B(5, 2) and its centroid is G(0, –3). Then, the coordinates of C are ______.

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Two vertices of ΔАBC are A(–1, 4) and B(5, 2) and its centroid is G(0, –3). Then, the coordinates of C are (–4, –15). Explanation: The centroid G of triangle ABC is `((x_A + x_B + x_C)/3, (y_A + y_B + y_C)/3)`. Using A(–1, 4), B(5, 2) and G(0, –3) gives x: (–1) + 5 + xC = 3 $\times$ 0 $\Rightarrow$ 4 + xC = 0 $\Rightarrow$ xC = –4 y: 4 + 2 + yC = 3 $\times$ (–3) $\Rightarrow$ 6 + yC = –9 $\Rightarrow$ yC = –15 So, C = (–4, –15).

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