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Консультация № 109355
14.11.2007, 11:18
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Аналитическая геометрия:
Дана прямая 2x+y-6=0 и на ней 2 точки A и B с координатами Ya=6, Yb=2. Написать ур-е высоты AD треугольника AOB (O-начало координат). И найти её длину.
Дана прямая 2x+y-6=0 и на ней 2 точки A и B с координатами Ya=6, Yb=2. Написать ур-е высоты AD треугольника AOB (O-начало координат). И найти её длину.
Обсуждение
Неизвестный
15.11.2007, 18:42
общий
это ответ
Здравствуйте, Petrosoft!
Найдём координаты точек A и B.
y=6 ⇒ 2x+6-6=0, 2x=0, x=0;
y=2 ⇒ 2x+2-6=0, 2x-4=0, x=2.
A(0;6), B(2;2).
Уравнение стороны BO:
x/2 = y/2,
x – y = 0.
Длина высоты AD — это расстояние от точки A до прямой BO. Вычисляется по формуле:
|AD| = |1*0 + (-1)*6|/√(1√2 + (-1)√2) = 6/√2 = 3√2.
Так как высота AD перпендикулярна стороне BO, то её уранвение имеет вид
AD: x + y + c = 0.
Подставим в это уравнение координаты точки A и получим:
0 + 6 + c = 0,
c = -6.
Ответ: AD: x + y – 6 = 0; |AD| = 3√2.
Найдём координаты точек A и B.
y=6 ⇒ 2x+6-6=0, 2x=0, x=0;
y=2 ⇒ 2x+2-6=0, 2x-4=0, x=2.
A(0;6), B(2;2).
Уравнение стороны BO:
x/2 = y/2,
x – y = 0.
Длина высоты AD — это расстояние от точки A до прямой BO. Вычисляется по формуле:
|AD| = |1*0 + (-1)*6|/√(1√2 + (-1)√2) = 6/√2 = 3√2.
Так как высота AD перпендикулярна стороне BO, то её уранвение имеет вид
AD: x + y + c = 0.
Подставим в это уравнение координаты точки A и получим:
0 + 6 + c = 0,
c = -6.
Ответ: AD: x + y – 6 = 0; |AD| = 3√2.
Форма ответа
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