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dashechka1707
dashechka1707
26.11.2020 12:11 •  Геометрия

Знайдіть відстань від точки А(-4;5;-8) до площини xy

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Ответ:
SnikerS205
SnikerS205
20.06.2020 02:15
ABC - равносторонний треугольник. A_1B_1C_1 - его проекция на плоскость P. AA_1=10,\;BB_1=15,\;CC_1=17.
Отложим на перпендикулярах отрезки B_1M=C_1N=AA_1=10 дм. Тогда BM = 15-10 = 5 дм, CM = 17-10 = 10 дм.
Точка О - центр ABC, т.е. точка пересечения его медиан. Медиана правильного треугольника ABC делится точкой O в соотношении AO:OD = 2:1, откуда AO:AD = 2:3
Опустим из точки D перпендикуляр на плоскость в точку D_1. Этот перпендикуляр разделит отрезок NM пополам. Значит AD_2 медиана треугольника AMN.
Отрезок DD_2 - средняя линия трапеции BCNM. Его длина \frac12(BM+CN)=\frac12(7+5)=\frac12\cdot12=6 дм.
Треугольники AOO_2\;u\;ADD_2 подобны по первому признаку: \angle A - общий, \angle O_2=\angle D_2=90^o.
Тогда 
OO_2:DD_2=AO:AD
OO_2:6=2:3\RightarrowOO_2=6\cdot2:3=4 дм.
Учитывая вышеизложенное, получаем 
OO_1=OO_2+O_1O_2=4+10=14 дм.

ответ: 14 дм.
Правильный треугольник спроектирован на плоскость,вершины его отстоят от плоскости на расстоянии 10д
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