Точка A — середина отрезка MK. Найдите координаты точки A и длину отрезка MK, если M (5; −2; 1), K (3; 4; −3). Отметьте верные ответы для точки А и отрезка МК : 1)MK=2√14. 2)MK=2√3. 3)A=(4;3;2). 4)A=(4;1;-1). 5)MK=2√11. 6)MK=8. 7)A=(-2;6;-4)
To find the coordinates of the midpoint A of the segment MK, we use the midpoint formula. The coordinates of A are given by:
\( A_x = \frac{M_x + K_x}{2}, A_y = \frac{M_y + K_y}{2}, A_z = \frac{M_z + K_z}{2} \)
Given points \( M (5; −2; 1) \), \( K (3; 4; −3) \), we calculate the coordinates of A:
\( A_x = \frac{5 + 3}{2} = 4 \) \( A_y = \frac{-2 + 4}{2} = 1 \) \( A_z = \frac{1 - 3}{2} = -1 \)
So the coordinates of A are (4; 1; -1).
To calculate the length of segment MK, we use the distance formula:
\( \text{Length of MK} = \sqrt{(K_x - M_x)^2 + (K_y - M_y)^2 + (K_z - M_z)^2} \)
Plugging in the coordinates of M and K:
\( \text{Length of MK} = \sqrt{(3 - 5)^2 + (4 - (-2))^2 + (-3 - 1)^2} \) \( \text{Length of MK} = \sqrt{(-2)^2 + (6)^2 + (-4)^2} \) \( \text{Length of MK} = \sqrt{4 + 36 + 16} \) \( \text{Length of MK} = \sqrt{56} \) \( \text{Length of MK} = 2\sqrt{14} \)
Now, let's match the answers:
- Correct: \( MK = 2\sqrt{14} \)
- Incorrect
- Incorrect
- Correct: A = (4; 1; -1)
- Incorrect
- Incorrect
- Incorrect
The correct answers are:
- MK = 2√14
- A = (4; 1; -1)
