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Консультация № 109087
12.11.2007, 17:10
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Провести перпендикуляр к прямой 2х-5y-10=0 через точку, отделяющую отрезок этой прямой между двумя осями координат в отношении 4:3
Помогите пожалуйста кто нибудь!
Помогите пожалуйста кто нибудь!
Обсуждение
Неизвестный
12.11.2007, 17:58
общий
это ответ
Здравствуйте, Caspersurgut!
Эта прямая пересекает ось Х в т. А с координатами (5, 0), а ось Y - в т. В с координатами (0, -2) => координаты вектора ВА(5, 2). Если разделить этот вектор на 7 одинаковых частей, и выбрать точку С, которая делила бы этот отрезок в отношении 4:3, то координаты вектора ВС будут (5*3/7, 2*3/7) = (15/7, 6/7) или же - второй вариант - (5*4/7, 2*4/7) = (20/7, 8/7) в зависимости от того, с какой стороны отрезка отделять меньшую часть.
И тогда координаты т.С будут = ОВ + ВС = (15/7, -8/7) или в случае второго варианта (20/7, -6/7)
Итак, требуется провести перпендикуляр СД к прямой через точку С. Нормальный вектор к этой прямой - (2, -5) (по условиям задачи, вроде бы не требуется вектор единичной длины?) => координаты т. Д (15/7+2t, -8/7-5t)
т.е. параметрическое задание перпендикулярной прямой x = 15/7+2t; y = -8/7-5t
или в случае второго варианта x = 20/7+2t; y = -6/7-5t
Эта прямая пересекает ось Х в т. А с координатами (5, 0), а ось Y - в т. В с координатами (0, -2) => координаты вектора ВА(5, 2). Если разделить этот вектор на 7 одинаковых частей, и выбрать точку С, которая делила бы этот отрезок в отношении 4:3, то координаты вектора ВС будут (5*3/7, 2*3/7) = (15/7, 6/7) или же - второй вариант - (5*4/7, 2*4/7) = (20/7, 8/7) в зависимости от того, с какой стороны отрезка отделять меньшую часть.
И тогда координаты т.С будут = ОВ + ВС = (15/7, -8/7) или в случае второго варианта (20/7, -6/7)
Итак, требуется провести перпендикуляр СД к прямой через точку С. Нормальный вектор к этой прямой - (2, -5) (по условиям задачи, вроде бы не требуется вектор единичной длины?) => координаты т. Д (15/7+2t, -8/7-5t)
т.е. параметрическое задание перпендикулярной прямой x = 15/7+2t; y = -8/7-5t
или в случае второго варианта x = 20/7+2t; y = -6/7-5t
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