Question

Середина отрезка AB лежит на оси Ox. Найдите m и n, если А(-6;m;10), B(4;-4;n). m = ? n = ?

Answer 1

Ответ:m=4 n= -10

Пошаговое объяснение:

Середина АВ с координатой х=(-6+4)÷2= -1, у=0, z=0

координаты А и В симметричны относительно этой середины.

А( -6; 4; 10)

В(4; -4; -10)

Answer 2

Given Information

We are given that the midpoint of line segment AB lies on the x-axis. The coordinates of point A are (-6, m, 10) and the coordinates of point B are (4, -4, n). We need to find the values of m and n.

Finding the Midpoint

To find the midpoint of line segment AB, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint (M) of a line segment with endpoints (x1, y1, z1) and (x2, y2, z2) are given by:

M = ((x1 + x2)/2, (y1 + y2)/2, (z1 + z2)/2)

In this case, the x-coordinate of the midpoint is given as 0 since it lies on the x-axis. So, we can set up the following equation:

0 = (-6 + 4)/2

Simplifying the equation, we get:

0 = -2/2

Therefore, the x-coordinate of the midpoint is 0.

Finding the y-coordinate of the midpoint (m)

To find the y-coordinate of the midpoint, we can equate the y-coordinates of points A and B to find the value of m. From point A, we have:

m = -4/2

Simplifying the equation, we get:

m = -2

Therefore, the y-coordinate of the midpoint is -2.

Finding the z-coordinate of the midpoint (n)

To find the z-coordinate of the midpoint, we can equate the z-coordinates of points A and B to find the value of n. From point A, we have:

10 = n/2

Simplifying the equation, we get:

n = 20

Therefore, the z-coordinate of the midpoint is 20.

Final Answer

Based on the calculations, we have found the values of m and n: - m = -2 - n = 20