Question

Даны координаты трёх точек A(3;5;3), B(3;5;1) и C(9;7;7). Вычисли медианы AD,BE,CF треугольника ABC. СРОЧНО ПОЖАЛУЙСТА​

Answer 1

Ответ:

Пошаговое объяснение:

Найдем середины сторон треугольника. для чего складываем соответств. координаты и и делим на два.

ВС -точку D(6;6;4)

х=(3+9)/2=6

у=(5+7)/2=6

z=(1+7)/2=4

AC-точку  E(6;6;5)

х=(3+9)/2=6

у=(5+7)/2=6

z=(3+7)/2=5

AB-точку F(3;5;2)

х=(3+3)/2=3

у=(5+3)/2=5

z=(3+1)/2=2

теперь. зная координаты начала и конца медиан найдем их длины, извлекая корень квадратный из суммы квадратов разности между началом и концом медианы.

АD=√((6-3)²+(6-5)²+(4-3)²)=√(9+1+1)=√11

BE=√((6-3)²+(6-5)²+(5-1)²)=√(9+1+16)=√26

CF=√((9-3)²+(7-5)²+(7-2)²)=√(36+4+25)=√65

Answer 2

Calculation of Medians of Triangle ABC

To calculate the medians of triangle ABC, we need to find the midpoints of each side of the triangle. The medians are the line segments that connect each vertex of the triangle to the midpoint of the opposite side.

Let's calculate the medians AD, BE, and CF step by step:

1. Calculate the midpoint of side BC: - The coordinates of point B are (3, 5, 1). - The coordinates of point C are (9, 7, 7). - To find the midpoint of BC, we can average the x, y, and z coordinates separately: - Midpoint of BC = ((3 + 9) / 2, (5 + 7) / 2, (1 + 7) / 2) = (6, 6, 4).

2. Calculate the midpoint of side AC: - The coordinates of point A are (3, 5, 3). - The coordinates of point C are (9, 7, 7). - To find the midpoint of AC, we can average the x, y, and z coordinates separately: - Midpoint of AC = ((3 + 9) / 2, (5 + 7) / 2, (3 + 7) / 2) = (6, 6, 5).

3. Calculate the midpoint of side AB: - The coordinates of point A are (3, 5, 3). - The coordinates of point B are (3, 5, 1). - To find the midpoint of AB, we can average the x, y, and z coordinates separately: - Midpoint of AB = ((3 + 3) / 2, (5 + 5) / 2, (3 + 1) / 2) = (3, 5, 2).

4. Calculate the medians AD, BE, and CF: - Median AD connects vertex A to the midpoint of BC. - Median BE connects vertex B to the midpoint of AC. - Median CF connects vertex C to the midpoint of AB.

Let's calculate the coordinates of each median:

- Median AD: - The coordinates of vertex A are (3, 5, 3). - The coordinates of the midpoint of BC are (6, 6, 4). - To find the coordinates of AD, we can average the x, y, and z coordinates separately: - Median AD = ((3 + 6) / 2, (5 + 6) / 2, (3 + 4) / 2) = (4.5, 5.5, 3.5).

- Median BE: - The coordinates of vertex B are (3, 5, 1). - The coordinates of the midpoint of AC are (6, 6, 5). - To find the coordinates of BE, we can average the x, y, and z coordinates separately: - Median BE = ((3 + 6) / 2, (5 + 6) / 2, (1 + 5) / 2) = (4.5, 5.5, 3).

- Median CF: - The coordinates of vertex C are (9, 7, 7). - The coordinates of the midpoint of AB are (3, 5, 2). - To find the coordinates of CF, we can average the x, y, and z coordinates separately: - Median CF = ((9 + 3) / 2, (7 + 5) / 2, (7 + 2) / 2) = (6, 6, 4.5).

Therefore, the coordinates of the medians AD, BE, and CF of triangle ABC are as follows:

- Median AD: (4.5, 5.5, 3.5) - Median BE: (4.5, 5.5, 3) - Median CF: (6, 6, 4.5)

I hope this helps! Let me know if you have any further questions.