\[\boxed{\mathbf{975.ОК\ ГДЗ - домашка\ на}\ 5}\]
\[Рисунок\ по\ условию\ задачи:\]
\[\mathbf{Дано:}\]
\[l:\ \ \ 3x - 4y + 12 = 0.\]
\[\mathbf{Найти:}\]
\[A(x;y);\]
\[B\left( x_{1};y_{1} \right).\]
\[\mathbf{Решение.}\]
\[1)\ Если\ l \cap OX = A,\ то\ A(x;0):\]
\[3x - 4 \bullet 0 + 12 = 0\]
\[3x = - 12\]
\[x = - 4\]
\[A( - 4;0).\]
\[2)\ Если\ l \cap OY = B,\ то\ B\left( 0;y_{1} \right):\]
\[3 \bullet 0 - 4y_{1} + 12 = 0\]
\[4y_{1} = 12\]
\[y_{1} = 3\]
\[B(0;3).\]
\[2)\ Начертим\ прямую\]
\[Ответ:\ A( - 4;0)\ и\ B(0;3).\]
\[\boxed{\mathbf{975}\mathbf{.еуроки - ответы\ на\ пятёрку}}\]
\[Рисунок\ по\ условию\mathbf{\ задачи:}\]
\[\mathbf{Дано:}\]
\[\mathrm{\Delta}DEF;\]
\[EG - медиана;\]
\[EO = OG;\]
\[\overrightarrow{a} = \overrightarrow{\text{ED}};\ \]
\[\overrightarrow{b} = \overrightarrow{\text{EF}}.\]
\[Выразить:\]
\(\overrightarrow{\text{DO}}\ через\ \overrightarrow{a}\ \ и\ \overrightarrow{b}\).
\[\mathbf{Решение.}\]
\[1)\ \overrightarrow{\text{ED}} + \overrightarrow{\text{DF}} = \overrightarrow{\text{EF}}\]
\[\overrightarrow{\text{DF}} = \overrightarrow{\text{EF}} - \overrightarrow{\text{ED}} = \overrightarrow{b} - \overrightarrow{a}.\]
\[2)\ \overrightarrow{\text{GE}} = \overrightarrow{\text{GD}} + \overrightarrow{\text{DE}} =\]
\[= - \frac{1}{2}\overrightarrow{\text{DF}} - \overrightarrow{\text{ED}} =\]
\[= - \frac{1}{2} \bullet \left( \overrightarrow{b} - \overrightarrow{a} \right) - \overrightarrow{a} =\]
\[= - \frac{1}{2}\overrightarrow{b} + \frac{1}{2}\overrightarrow{a} - \overrightarrow{a} = - \frac{1}{2}\overrightarrow{b} - \frac{1}{2}\overrightarrow{a}.\]
\[3)\ \overrightarrow{\text{DO}} = \overrightarrow{\text{DG}} + \overrightarrow{\text{GO}} =\]
\[= \frac{1}{2}\overrightarrow{\text{DF}} + \frac{1}{2}\overrightarrow{\text{GE}} =\]
\[= \frac{1}{2} \bullet \left( \overrightarrow{b} - \overrightarrow{a} \right) + \frac{1}{2} \bullet \left( - \frac{1}{2}\overrightarrow{b} - \frac{1}{2}\overrightarrow{a} \right) =\]
\[= \frac{1}{2}\overrightarrow{b} - \frac{1}{2}\overrightarrow{a} - \frac{1}{4}\overrightarrow{b} - \frac{1}{4}\overrightarrow{a} =\]
\[= \frac{1}{4}\overrightarrow{b} - \frac{3}{4}\ \overrightarrow{a}.\]
\[Ответ:\ \overrightarrow{\text{DO}} = \frac{1}{4}\overrightarrow{b} - \frac{3}{4}\ \overrightarrow{a}.\]