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Консультация № 109664
16.11.2007, 11:11
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Здравствуйте вот мой вопрос . Даны координаты вершин (x1 x2 x3 x4 y1 y2 y3 y4) четырехьугольника угольника,определить явл. ли этот 4-х угольник равнобокой трапецией.
на этот вопрос мне нужны только формулы! Заранее спасибо,
на этот вопрос мне нужны только формулы! Заранее спасибо,
Обсуждение
Неизвестный
16.11.2007, 12:32
общий
это ответ
Здравствуйте, Князь Владимир!
Для этого сначала находим равные стороны. Для этого ищем длину каждой стороны
12=((x2-x1)^2 + (y2-y1)^2)
если равных сторон нет, то точно не равнобокая трапеция :)
если все четыре стороны равны, то равнобокая трапеция (квадрат или ромб)
если есть две равные противоложные стороны, например
12 и 34 или 41 и 23, то берем оставшуюся пару и проверяем ее на параллельность.
Например, равны оказались отрезки 12 и 34.
Тогда проверяем, параллельны ли отрезки 41 и 23. Для этого сотавляем уравнения прямых y = kx+b или (x-x2)/(x3-x2)=(y-y2)/(y3-y2). Для второй прямой аналогично. В первом случае смотрим, чтоб коэффициенты k были равны, а b различны, во втором случае составляем систему и проверяем, есть ли решение, если решение есть, значит они не параллельные, значит не трапеция.
Для этого сначала находим равные стороны. Для этого ищем длину каждой стороны
12=((x2-x1)^2 + (y2-y1)^2)
если равных сторон нет, то точно не равнобокая трапеция :)
если все четыре стороны равны, то равнобокая трапеция (квадрат или ромб)
если есть две равные противоложные стороны, например
12 и 34 или 41 и 23, то берем оставшуюся пару и проверяем ее на параллельность.
Например, равны оказались отрезки 12 и 34.
Тогда проверяем, параллельны ли отрезки 41 и 23. Для этого сотавляем уравнения прямых y = kx+b или (x-x2)/(x3-x2)=(y-y2)/(y3-y2). Для второй прямой аналогично. В первом случае смотрим, чтоб коэффициенты k были равны, а b различны, во втором случае составляем систему и проверяем, есть ли решение, если решение есть, значит они не параллельные, значит не трапеция.
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