ГДЗ по геометрии 7 класс Атанасян Задание 974

\[\boxed{\mathbf{974.ОК\ ГДЗ - домашка\ на}\ 5}\]

\[Рисунок\ по\ условию\ задачи:\]

\[\mathbf{Дано:}\]

\[A( - 2; - 2);\]

\[B( - 3;1);\]

\[C(7;7);D(3;1)\]

\[MN - средняя\ линия.\]

\[\mathbf{Написать:}\]

\[уравнения\ прямых\]

\[\textbf{а)}\ \text{AC\ }и\ BD;\]

\[\textbf{б)}\ MN.\]

\[\mathbf{Решение.}\]

\[\textbf{а)}\ 1)\ A( - 2; - 2):\]

\[ax + by + c = 0;\]

\[a \bullet ( - 2) + b \bullet ( - 2) + c = 0;\]

\[- 2a - 2b + c = 0;\ \]

\[- 2a = 2b - c;\]

\[a = \frac{c - 2b}{2} = \frac{c}{2} - b.\]

\[C(7;7):\]

\[ax + by + c = 0;\]

\(7a + 7b + c = 0;7a = - 7b - c;\)

\[a = \frac{- 7b - c}{7} = - b - \frac{c}{7};\]

\[- b - \frac{c}{7} = \frac{c}{2} - b\]

\[\left\{ \begin{matrix} c = 0 \\ a = - b \\ \end{matrix} \right.\ .\]

\[2)\ Уравнение\ прямой\ AC:\]

\[\left. \ ax - ay + 0 = 0\ \ \ \ \ \ \ \ \right|:a\]

\[x - y = 0.\]

\[3)\ B( - 3;1):\]

\[ax + by + c = 0;\]

\[- 3a + b + c = 0;\]

\[a = \frac{b + c}{3}.\]

\[D(3;1):\]

\[ax + by + c = 0;\]

\[3a + b + c = 0;\]

\[b = - 3a - c;\]

\[a = \frac{- 3a - c + c}{3} = - a\]

\[a = 0 \Longrightarrow b = - c.\]

\[4)\ Уравнение\ прямой\ BD:\]

\[ax + by + c = 0\]

\[- cy + c = 0\ \ \ \ |\ :c\]

\[- y + 1 = 0.\]

\[3)\ N(5;4):\]

\[5a + 4b + c = 0\]

\[a = \frac{- 4b - c}{5}.\]

\[M( - 2,5; - 0,5):\ \]

\[\left. \ - \frac{5}{2}a - \frac{1}{2}b + c = 0 \right| \bullet 2\]

\[- 5a - b + 2c = 0;b = 2c - 5a\]

\[b = 2c - ( - 4b + c) =\]

\[= 2c + 4b + c + 4b\]

\[- 3b = 3c\]

\[b = - c \Longrightarrow a = \frac{3}{5}\text{c.}\]

\[4)\ Уравнение\ прямой\ MN:\]

\[\left. \ \frac{3}{5}cx - cy + c = 0 \right| \bullet \frac{5}{c}\]

\[3x - 5y + 5 = 0.\]

\[Ответ:\ а)\ x - y = 0\ и\ \]

\[- y + 1 = 0;\ \]

\[\textbf{б)}\ 3x - 5y + 5 = 0.\]