Trong mặt phẳng tọa độ Oxy, cho tam giác ABC có

C

- Hướng dẫn giải

Dễ thấy \(\frac{{{S_{\Delta ABC}}}}{{{S_{\Delta ABM}}}} = 4 \Leftrightarrow \frac{{BC}}{{BM}} = 4 \Leftrightarrow \left[ \begin{array}{l}\overrightarrow {BC} = 4\overrightarrow {BM} \\\overrightarrow {BC} = - 4\overrightarrow {BM} \end{array} \right.\).

TH1: \(\overrightarrow {BC} = 4\overrightarrow {BM} \) thì: \(\left\{ \begin{array}{l}x - 2 = - \frac{3}{4}\\y - 1 = - \frac{3}{4}\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}x = \frac{5}{4}\\y = \frac{1}{4}\end{array} \right. \Rightarrow x.y = \frac{5}{{16}}\).

TH2: \(\overrightarrow {BC} = - 4\overrightarrow {BM} \) thì: \(\left\{ \begin{array}{l}x - 2 = \frac{3}{4}\\y - 1 = \frac{3}{4}\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}x = \frac{{11}}{4}\\y = \frac{7}{4}\end{array} \right. \Rightarrow x.y = \frac{{77}}{{16}}\).