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Консультация № 201209
22.06.2021, 13:42
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Здравствуйте! Прошу помощи в следующем вопросе:
Даны уравнения сторон треугольника x+2y+1=0; 2x-y-2=0; 2x+y+2=0.
Найти точку пересечения высот.
Даны уравнения сторон треугольника x+2y+1=0; 2x-y-2=0; 2x+y+2=0.
Найти точку пересечения высот.
Обсуждение
22.06.2021, 15:32
общий
это ответ
Здравствуйте, verunymel!
Даны уравнения сторон треугольника x+2y+1=0; 2x-y-2=0; 2x+y+2=0.
Найти точку пересечения высот.
Перепишем сначала уравнения сторон так:
Вычислим координаты точек пересечения:
-- первой прямой со второй:
-- первой прямой с третьей:
Выведем уравнение прямой, которая содержит высоту треугольника, перпендикулярную третьей стороне. Эта прямая проходит через точку
поэтому
Выведем уравнение прямой, которая содержит высоту треугольника, перпендикулярную второй стороне. Эта прямая проходит через точку
поэтому
Вычислим координаты точки пересечения двух последних прямых:
Следовательно высоты треугольника пересекаются в точке
В прикреплённом файле заданный треугольник показан заливкой серого цвета.
Даны уравнения сторон треугольника x+2y+1=0; 2x-y-2=0; 2x+y+2=0.
Найти точку пересечения высот.
Перепишем сначала уравнения сторон так:
Вычислим координаты точек пересечения:
-- первой прямой со второй:
-- первой прямой с третьей:
Выведем уравнение прямой, которая содержит высоту треугольника, перпендикулярную третьей стороне. Эта прямая проходит через точку
поэтомуВыведем уравнение прямой, которая содержит высоту треугольника, перпендикулярную второй стороне. Эта прямая проходит через точку
поэтомуВычислим координаты точки пересечения двух последних прямых:
Следовательно высоты треугольника пересекаются в точке
В прикреплённом файле заданный треугольник показан заливкой серого цвета.
Прикрепленные файлы:
5
Огромное спасибо)
Об авторе:
Facta loquuntur.
Facta loquuntur.
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