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Консультация № 137541
19.05.2008, 17:26
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Уважаемые эксперты! Помогите, пожалуйста, решить задачу по высшей математике...
Задача: Даны координаты вершины треугольника.
Сделать вывод:
1. Уравнение стороны АВ.
2. Уравнение высоты СН, точку пересечения стороны АВ и высоты СН.
3. Уравнение прямой, проходящей через вершину С паралельно стороне АВ.
4. Длину АВ.
А(-1,-4); В(9,6); С(-5,4);
Добавляйте коментарии к вычеслениям...
Заранее спасибо...
Задача: Даны координаты вершины треугольника.
Сделать вывод:
1. Уравнение стороны АВ.
2. Уравнение высоты СН, точку пересечения стороны АВ и высоты СН.
3. Уравнение прямой, проходящей через вершину С паралельно стороне АВ.
4. Длину АВ.
А(-1,-4); В(9,6); С(-5,4);
Добавляйте коментарии к вычеслениям...
Заранее спасибо...
Обсуждение
Неизвестный
19.05.2008, 21:24
общий
это ответ
Здравствуйте, Уманский Денис!
1. (x-(-1))/(9-(-1)) = (y-(-4))/(6-(-4))
(x+1)/10 = (y+4)/10
x + 1 = y + 4
y = x - 3 - уравнение АВ
2. Для прямой перпендикулярной АВ угловой коэффициент будет равен -1.
Таким образом, уравнение СН будет иметь вид у = - х + b
Подставим координаты точки С:
4 = 5 + b
b = -1
CH: y = -x - 1
Для того, чтобы найти точку пересечения сложим равенства для АВ и СН:
2у = -4
у = -2
подставим в уравнение для АВ:
-2 = х - 3
х = 1
Точка пересечения (1; -2)
3. Уравнение прямой параллельной АВ будет иметь тот же угловой коэффициент, то есть вид:
у = х + b
подставим координаты С:
4 = b - 5
b = 9
То есть уравнение у = х + 9
4. АВ = √((-1-9)^2 + (-4-6)^2)
AB = 10√2
1. (x-(-1))/(9-(-1)) = (y-(-4))/(6-(-4))
(x+1)/10 = (y+4)/10
x + 1 = y + 4
y = x - 3 - уравнение АВ
2. Для прямой перпендикулярной АВ угловой коэффициент будет равен -1.
Таким образом, уравнение СН будет иметь вид у = - х + b
Подставим координаты точки С:
4 = 5 + b
b = -1
CH: y = -x - 1
Для того, чтобы найти точку пересечения сложим равенства для АВ и СН:
2у = -4
у = -2
подставим в уравнение для АВ:
-2 = х - 3
х = 1
Точка пересечения (1; -2)
3. Уравнение прямой параллельной АВ будет иметь тот же угловой коэффициент, то есть вид:
у = х + b
подставим координаты С:
4 = b - 5
b = 9
То есть уравнение у = х + 9
4. АВ = √((-1-9)^2 + (-4-6)^2)
AB = 10√2
Форма ответа
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