Решебник по геометрии 9 класс Мерзляк Задание 303

\[1)\ A( - 2;\ - 7),\ B( - 1;\ - 4),\ C(5;\ 14):\]

\[AB = \sqrt{( - 2 + 1)^{2} + ( - 7 + 4)^{2}} =\]

\[= \sqrt{1 + 9} = \sqrt{10};\]

\[BC = \sqrt{( - 1 - 5)^{2} + ( - 4 - 14)^{2}} =\]

\[= \sqrt{36 + 324} = 6\sqrt{10};\]

\[AC = \sqrt{( - 2 - 5)^{2} + ( - 7 - 14)^{2}} =\]

\[= \sqrt{49 + 441} = 7\sqrt{10};\]

\[AC = AB + BC.\]

\[Ответ:\ \ B.\]

\[2)\ D( - 1;\ 3),\ E(2;\ 13),\ F(5;\ 21):\]

\[DE = \sqrt{( - 1 - 2)^{2} + (3 - 13)^{2}} =\]

\[= \sqrt{9 + 100} = \sqrt{109};\]

\[EF = \sqrt{(2 - 5)^{2} + (13 - 21)^{2}} =\]

\[= \sqrt{9 + 64} = \sqrt{73};\]

\[DF = \sqrt{( - 1 - 5)^{2} + (3 - 21)^{2}} =\]

\[= \sqrt{36 + 324} = \sqrt{360};\]

\[DF \neq DE + EF.\]

\[Ответ:\ \ нет.\]