Triangle ABC has its centroid at point G(4, 5), and vertex A is located at (2, 3). If point D is the midpoint of side BC, what are the coordinates of D?
(5, 6)
The centroid divides the median AD in the ratio 2 : 1 from vertex A.
\(G = \dfrac{{A + 2D}}{{3}} \implies 3G = A + 2D \implies D = \dfrac{{3G - A}}{{2}}\)
\(D_x = \dfrac{{3(4) - 2}}{{2}} = \dfrac{{10}}{{2}} = 5\)
\(D_y = \dfrac{{3(5) - 3}}{{2}} = \dfrac{{12}}{{2}} = 6\)
D = (5, 6)
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