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Консультация № 181028
29.11.2010, 21:28
0.00 руб.
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Здравствуйте, уважаемые эксперты! Прошу Вас ответить на следующий вопрос:
дано
треугольник ABC с координатами A (2 ; -2) B (5 ; 2) C (6 ; 0) D (4,4 ; 1,2) E (5,5 ; 1)
уравнение прямой AB: 4x-3y-14=0
уравнение прямой CD: 3x+4y-18=0
найти нужно
уравнение прямой проходящей через точку E параллельно стороне AB и точку M (точку пересечения прямой с высотой CD)
Приложение:
дано
треугольник ABC с координатами A (2 ; -2) B (5 ; 2) C (6 ; 0) D (4,4 ; 1,2) E (5,5 ; 1)
уравнение прямой AB: 4x-3y-14=0
уравнение прямой CD: 3x+4y-18=0
найти нужно
уравнение прямой проходящей через точку E параллельно стороне AB и точку M (точку пересечения прямой с высотой CD)
Приложение:
Обсуждение
29.11.2010, 23:04
общий
это ответ
Здравствуйте, Посетитель - 348442!
Если я правильно понял задачу, то решаем так: уравнение прямой, параллельной AB имеет вид
4x-3y+С=0
Постоянная C находится из условия прохождения через точку E: 4*5,5-3*1+C=0 ---> C=-19. Искомое уравнение
4x-3y-19=0
Точку пересечения находим, решая систему
4x-3y-19=0
3x+4y-18=0
12x-9y-57=0
12x+16y-72=0
Вычитая уравнения, находим 25y=15 ---> y=3/5
x=(18-4y)/3=26/5
Точка M(26/5;3/5)
Если я правильно понял задачу, то решаем так: уравнение прямой, параллельной AB имеет вид
4x-3y+С=0
Постоянная C находится из условия прохождения через точку E: 4*5,5-3*1+C=0 ---> C=-19. Искомое уравнение
4x-3y-19=0
Точку пересечения находим, решая систему
4x-3y-19=0
3x+4y-18=0
12x-9y-57=0
12x+16y-72=0
Вычитая уравнения, находим 25y=15 ---> y=3/5
x=(18-4y)/3=26/5
Точка M(26/5;3/5)
29.11.2010, 23:20
общий
это ответ
Здравствуйте, Посетитель - 348442!
Уравнение прямой находим по формуле: Y-Yo=k(X-Xo)
т.к. искомая прямая || пр.АВ, ее угловой коэффициент находим из уравнения пр АВ
4x-3y-14=0 ; 3y=4x-14; y=4/3x-14/3 ; k=4/3
Искомое уравнение прямой: y-1=4/3(x-5.5)=> 3y-3=4x-22; 4x-3y-19=0-искомое уравнение прямой.
Чтобы найти координаты точки М, решим систему уравнений
4x-3y-19=0 16x-12y-76=0
3x+4y-18=0 => +
9x+12y-54=0
25x=130 => x=130/25=5.2; y=(4x-19)/3=(20.8-19)/3=1.8/3=0.6 Ответ: ур-ние прямой: 4x-3y-19=0; M(5.2; 0.6)
Уравнение прямой находим по формуле: Y-Yo=k(X-Xo)
т.к. искомая прямая || пр.АВ, ее угловой коэффициент находим из уравнения пр АВ
4x-3y-14=0 ; 3y=4x-14; y=4/3x-14/3 ; k=4/3
Искомое уравнение прямой: y-1=4/3(x-5.5)=> 3y-3=4x-22; 4x-3y-19=0-искомое уравнение прямой.
Чтобы найти координаты точки М, решим систему уравнений
4x-3y-19=0 16x-12y-76=0
3x+4y-18=0 => +
9x+12y-54=0
25x=130 => x=130/25=5.2; y=(4x-19)/3=(20.8-19)/3=1.8/3=0.6 Ответ: ур-ние прямой: 4x-3y-19=0; M(5.2; 0.6)
Форма ответа
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