Question

Найдите длину медианы проведённой из вершины С в треугольнике С(2;2),D(6;5),E(5;-2).Пожалуйста, очень срочно.

Answer 1

Длина вектора СD составит корень((6-2)^2+(5-2)^2)=корень(16+9)=5
длина вектора EC составит корень((5-2)^2+(-2-2)^2)=корень(9+16)=5
значит треугольник равнобедренныйдлина вектора СD составит корень((6-2)^2+(5-2)^2)=корень(16+9)=5
длина вектора EC составит корень((5-2)^2+(-2-2)^2)=корень(9+16)=5
значит треугольник равнобедренный
Дальше координата середины ED x=(6+5)/2=5.5; Y=(5-2)/2=1.5
Находим длину высоты корень((5,5-2)^2+(1,5-2)^2)=корень(12,25+0,25)=примерно 3,54

Answer 2

Finding the Length of the Median in Triangle CDE

To find the length of the median drawn from vertex C in triangle CDE, we can use the formula for the length of a median in a triangle. The length of the median from vertex C can be calculated using the following formula:

Length of Median from C = (1/2) * sqrt(2 * (|DE|^2 + |DC|^2) - |CE|^2)

Where: - |DE| represents the length of side DE - |DC| represents the length of side DC - |CE| represents the length of side CE

Let's calculate the length of the median using the given coordinates for points C, D, and E.

Calculating the Length of Median from C

Given the coordinates: C(2, 2) D(6, 5) E(5, -2)

We can calculate the lengths of the sides using the distance formula: - |DE| = sqrt((5 - 6)^2 + (-2 - 5)^2) - |DC| = sqrt((6 - 2)^2 + (5 - 2)^2) - |CE| = sqrt((5 - 2)^2 + (-2 - 2)^2)

Calculating the lengths of the sides: - |DE| = sqrt((-1)^2 + (-7)^2) = sqrt(1 + 49) = sqrt(50) - |DC| = sqrt((4)^2 + (3)^2) = sqrt(16 + 9) = sqrt(25) = 5 - |CE| = sqrt((3)^2 + (4)^2) = sqrt(9 + 16) = sqrt(25) = 5

Now, we can substitute these values into the formula for the length of the median from C: Length of Median from C = (1/2) * sqrt(2 * (|DE|^2 + |DC|^2) - |CE|^2)

Length of Median from C = (1/2) * sqrt(2 * (50 + 25) - 25) Length of Median from C = (1/2) * sqrt(2 * 75 - 25) Length of Median from C = (1/2) * sqrt(150 - 25) Length of Median from C = (1/2) * sqrt(125) Length of Median from C = (1/2) * 5 * sqrt(5) Length of Median from C = 5/2 * sqrt(5)

So, the length of the median drawn from vertex C in triangle CDE is 5/2 * sqrt(5).