\[\boxed{\mathbf{996.ОК\ ГДЗ - домашка\ на}\ 5}\]
\[Рисунок\ по\ условию\ задачи:\]
\[\mathbf{Дано:}\]
\[\mathrm{\Delta}ABC;\]
\[A( - 5;13);B(3;5);\]
\[C( - 3; - 1);\]
\[M,N,K - середины\ сторон.\]
\[\mathbf{Найти:}\]
\[\textbf{а)}\ координаты - \ M,N\ и\ K;\]
\[\textbf{б)}\ BK;\]
\[\textbf{в)}\ MN;MK;NK.\]
\[\mathbf{Решение.}\]
\[\textbf{б)}\ BK = \sqrt{(3 + 4)^{2} + (5 - 6)^{2}} =\]
\[= \sqrt{50} = 5\sqrt{2}.\]
\[\textbf{в)}\ 1)\ MN =\]
\[= \sqrt{( - 1 - 0)^{2} + (9 - 2)^{2}} =\]
\[= \sqrt{50} = 5\sqrt{2};\]
\[2)\ MK =\]
\[= \sqrt{( - 1 + 4)^{2} + (9 - 6)^{2}} =\]
\[= \sqrt{18} = 3\sqrt{2};\]
\[3)\ NK = \sqrt{(0 + 4)^{2} + (2 - 6)^{2}} =\]
\[= \sqrt{32} = 4\sqrt{2}.\]
\[Ответ:а)\ M( - 1;9);\ N(0;2);\ \]
\[K( - 4;6);\]
\[\textbf{б)}\ \ BK = \ 5\sqrt{2};\]
\[\textbf{в)}\ MN = 5\sqrt{2};MK = 3\sqrt{2};\]
\(NK = 4\sqrt{2}.\)