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Консультация № 109053
12.11.2007, 13:04
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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
Обсуждение
Неизвестный
17.11.2007, 10:44
общий
это ответ
Здравствуйте, Caspersurgut!
Провести перпендикуляр к прямой 2х-5y-10=0 через точку, отделяющую отрезок этой прямой между двумя осями координат в отношении 4:3
Перпендикуляры к 2x - 5y - 10 = 0 имеют вид 5x + 2y = c.
Точки пересечения с осями координат: x = c/5, y = 0 и x = 0, y = с/2.
Точки которые делят отрезок между этими точками в отношении 3:4 имеют координаты (c/5*4/7, c/2*3/7) либо (c/5*3/7, c/2*4/7).
Они должны приадлежать 2х-5y-10=0.
Подставляем первую точку 2*c/5*4/7 - 5*c/2*3/7 - 10 = 0, c = -700/59. Уравнение 5x + 2y + 700/59 = 0.
Подставляем вторую точку 2*c/5*3/7 - 5*c/2*4/7 - 10 = 0, c = -175/22. Уравнение 5x + 2y + 175/22 = 0.
Проверьте вычисления
Провести перпендикуляр к прямой 2х-5y-10=0 через точку, отделяющую отрезок этой прямой между двумя осями координат в отношении 4:3
Перпендикуляры к 2x - 5y - 10 = 0 имеют вид 5x + 2y = c.
Точки пересечения с осями координат: x = c/5, y = 0 и x = 0, y = с/2.
Точки которые делят отрезок между этими точками в отношении 3:4 имеют координаты (c/5*4/7, c/2*3/7) либо (c/5*3/7, c/2*4/7).
Они должны приадлежать 2х-5y-10=0.
Подставляем первую точку 2*c/5*4/7 - 5*c/2*3/7 - 10 = 0, c = -700/59. Уравнение 5x + 2y + 700/59 = 0.
Подставляем вторую точку 2*c/5*3/7 - 5*c/2*4/7 - 10 = 0, c = -175/22. Уравнение 5x + 2y + 175/22 = 0.
Проверьте вычисления
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