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Консультация № 64766
29.11.2006, 15:31
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Помогите решить, пожалуйста!
Даны вершины A(x1,y1), B(x2,y2), С(хЗ,уЗ) треугольника ABC. Требуется найти:
1) общее уравнение прямой АВ,
2) общее уравнение прямой, на которой лежит высота СН и длину этой высоты;
3) общее уравнение прямой, на которой лежит медиана AM,
4) точку N пересечения медианы AM и СН,
5) параметрическое уравнение прямой,
параллельной стороне АВ и проходящей через вершину С,
6) косинус внутреннего угол при вершине А.
Значения радикалов и отношений вычислить с точностью до второго знака.
А(-8,-1), В(4,6), С(-4,0).
Даны вершины A(x1,y1), B(x2,y2), С(хЗ,уЗ) треугольника ABC. Требуется найти:
1) общее уравнение прямой АВ,
2) общее уравнение прямой, на которой лежит высота СН и длину этой высоты;
3) общее уравнение прямой, на которой лежит медиана AM,
4) точку N пересечения медианы AM и СН,
5) параметрическое уравнение прямой,
параллельной стороне АВ и проходящей через вершину С,
6) косинус внутреннего угол при вершине А.
Значения радикалов и отношений вычислить с точностью до второго знака.
А(-8,-1), В(4,6), С(-4,0).
Обсуждение
Неизвестный
29.11.2006, 16:14
общий
это ответ
Здравствуйте, Mashenka!
1)
(x- x1)/(x2-x1) = (y-y1)/(y2-y1) - общее уравнение прямой, проходящей через точки
(x1,y1) и (x2,y2)
2)
H (x,y) -основание высоты
вектор СН = (x - xc, y - yc),
вектор AH = (x - xa, y - ya).
Т.к. они перпендикулярны (СН - высота), => CH * AH = 0 (скалярное произведение)
=> (x - xc)*(x - xa) +(y - yc)*( y - ya) = 0
Далее, т.к. H принадлежит прямой AB - получим для x и y второе уравнение.
Решаем систему двух уравнений, затем полученные значение в 1) с координатами С.
Длина высоты по формуле d^2 = (x1-x2)^2 + (y1-y2)^2
3)
xm=(x1+x2)/2; ym=(y1+y2)/2 - координаты середины отрезка, далее см. 1)
4)
Точки М и H как в 3) далее 1) для AM и СН, затем система уравнений.
5) sorry!
6) по теореме косинусов (длины сторон по формуле в 2).
Удачи!
1)
(x- x1)/(x2-x1) = (y-y1)/(y2-y1) - общее уравнение прямой, проходящей через точки
(x1,y1) и (x2,y2)
2)
H (x,y) -основание высоты
вектор СН = (x - xc, y - yc),
вектор AH = (x - xa, y - ya).
Т.к. они перпендикулярны (СН - высота), => CH * AH = 0 (скалярное произведение)
=> (x - xc)*(x - xa) +(y - yc)*( y - ya) = 0
Далее, т.к. H принадлежит прямой AB - получим для x и y второе уравнение.
Решаем систему двух уравнений, затем полученные значение в 1) с координатами С.
Длина высоты по формуле d^2 = (x1-x2)^2 + (y1-y2)^2
3)
xm=(x1+x2)/2; ym=(y1+y2)/2 - координаты середины отрезка, далее см. 1)
4)
Точки М и H как в 3) далее 1) для AM и СН, затем система уравнений.
5) sorry!
6) по теореме косинусов (длины сторон по формуле в 2).
Удачи!
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