Question

СРОЧНО!ИзобразитесистемукоординатOxyzипостройтеточкуA(1; —2; -4).Найдите расстояние от этой точки до координатных плоскостейЧЕРТЕЖ ПОДРОБНЫЙ С ОБЬЯСНЕНИЯМИ

Answer 1

ИзобразитесистемукоординатOxyzипостройтеточкуA(1; —2; -4).
смотри во вложении

Найдите расстояние от этой точки до координатных плоскостей

от А до ху расстояние 4 (равно модулю координаты по оси z)
от А до хz расстояние 2(равно модулю координаты по оси y)
от А до yz расстояние 1(равно модулю координаты по оси x)

Answer 2

1. На оси х сдвигаемся на 1 единицу в положительном направлении
2. Через текущую точку (точку, в которой находимся в данный момент) (1; 0; 0) проведем прямую, параллельную оси у - обозначим ее у`
3. На оси у` сдвигаемся на 2 единицы в отрицательном направлении
4. Через текущую точку (1; -2; 0) проведем прямую, параллельную оси z - обозначим ее z`
5. На оси z` сдвигаемся на 4 единицы в отрицательном направлении. Получим искомую точку А(1; -2; -4)

При построении мы сдвинулись по оси х на 1 единицу - значит расстояние до плоскости yOz равно 1. Аналогично, сдвиг по оси y||y` на 2 единицы - расстояние до плоскости xOz равно 2, сдвиг по оси z||z` на 4 единицы - расстояние до плоскости xOy равно 4

Answer 3

System of Coordinates and Point A(1, -2, -4)

To answer your question, let's start by understanding the system of coordinates and the given point A(1, -2, -4).

A system of coordinates is a way to represent points in space using numerical values. The most common system of coordinates is the Cartesian coordinate system, which uses three perpendicular axes: the x-axis, y-axis, and z-axis. These axes intersect at the origin, denoted as O.

In the Cartesian coordinate system, each point is represented by an ordered triple (x, y, z), where x represents the distance along the x-axis, y represents the distance along the y-axis, and z represents the distance along the z-axis.

Now, let's plot the point A(1, -2, -4) on the coordinate system:

- The x-coordinate of point A is 1, which means it is located 1 unit to the right of the origin along the x-axis. - The y-coordinate of point A is -2, which means it is located 2 units below the origin along the y-axis. - The z-coordinate of point A is -4, which means it is located 4 units behind the origin along the z-axis.

Therefore, point A(1, -2, -4) can be plotted as follows: - The point is 1 unit to the right of the origin along the x-axis. - The point is 2 units below the origin along the y-axis. - The point is 4 units behind the origin along the z-axis.

Distance from Point A to Coordinate Planes

To find the distance from point A(1, -2, -4) to the coordinate planes, we need to calculate the perpendicular distances from the point to each plane.

The coordinate planes are: 1. The xy-plane: This plane is formed by the x-axis and y-axis. 2. The xz-plane: This plane is formed by the x-axis and z-axis. 3. The yz-plane: This plane is formed by the y-axis and z-axis.

Let's calculate the distances from point A to each of these planes:

1. Distance from point A to the xy-plane: - The xy-plane is perpendicular to the z-axis. - The z-coordinate of point A is -4. - Therefore, the distance from point A to the xy-plane is |-4| = 4 units.

2. Distance from point A to the xz-plane: - The xz-plane is perpendicular to the y-axis. - The y-coordinate of point A is -2. - Therefore, the distance from point A to the xz-plane is |-2| = 2 units.

3. Distance from point A to the yz-plane: - The yz-plane is perpendicular to the x-axis. - The x-coordinate of point A is 1. - Therefore, the distance from point A to the yz-plane is |1| = 1 unit.

In summary, the distances from point A(1, -2, -4) to the coordinate planes are as follows: - Distance to the xy-plane: 4 units - Distance to the xz-plane: 2 units - Distance to the yz-plane: 1 unit.

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