Question

Coordinates grid

Answer 1

A coordinates grid, often referred to as a Cartesian coordinate system, is a mathematical system used to specify points in a two-dimensional (2D) or three-dimensional (3D) space using numerical coordinates.

### 2D Cartesian Coordinate System

In a 2D grid, points are defined by two coordinates \((x, y)\):

- **X-axis**: The horizontal line, where the value of \(x\) increases from left to right.
- **Y-axis**: The vertical line, where the value of \(y\) increases as you move up.

#### Example Points:
- The point \((3, 2)\) is located 3 units to the right of the origin (0, 0) and 2 units up.
- The point \((-1, -4)\) is located 1 unit to the left of the origin and 4 units down.

### 3D Cartesian Coordinate System

In a 3D grid, points are defined by three coordinates \((x, y, z)\):

- **X-axis**: Horizontal line, similar to the 2D plane.
- **Y-axis**: Vertical line, also similar to the 2D plane.
- **Z-axis**: Depth line, which comes out of the plane in the positive direction and goes back in the negative direction (or vice versa).

#### Example Points:
- The point \((2, 3, 5)\) is located 2 units along the x-axis, 3 units along the y-axis, and 5 units along the z-axis.

### Quadrants in 2D
A 2D Cartesian plane is divided into four quadrants:
1. **Quadrant I**: \(x > 0\), \(y > 0\)
2. **Quadrant II**: \(x < 0\), \(y > 0\)
3. **Quadrant III**: \(x < 0\), \(y < 0\)
4. **Quadrant IV**: \(x > 0\), \(y < 0\)

### Applications
Coordinate grids are used in various fields, such as physics, engineering, computer graphics, and geography, to represent and analyze spatial relationships.