Вопрос школьника по предмету Геометрия
Координаты вершин треугольника A(6;5),B(2;-4)C(-2;-1)Найдите длины его медиан
Ответ учителя по предмету Геометрия
1) Основания медиан (точки пересечения медиан со сторонами). А₁(Ха1;Уа1) ((Хв+Хс)/2; (Ув+Ус)/2)
x y
А₁ 0 -2,5.
В₁(Хв1;Ув1) ((Ха+Хс)/2; (Уа+Ус)/2)
х у
В₁ 2 2.
C₁(Хс1;Ус1) ((Ха+Хв)/2; (Уа+Ув)/2)
х у
С₁ 4 0,5.
2) Длины медиан:
АА₁ = √((Ха1-Ха)²+(Уа1-Уа)²)) = √
92.25 ≈
9.604686356,
BB₁ = √((Хв1-Хв)²+(Ув1-Ув)²)) = √36 =
6,
CC₁ = √((Хc1-Хc)²+(Уc1-Уc)²)) = √
38.25 ≈ 6.184658438.
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