The Cartesian coordinate system is an essential tool in geometry that allows us to locate points in a two-dimensional space using two perpendicular number lines. In this article, we will explore the basics of the Cartesian coordinate system and how it can be used in geometry.
What is the Cartesian Coordinate System?
The Cartesian coordinate system, also known as the rectangular coordinate system. It is a mathematical system that uses two perpendicular number lines, the x-axis and the y-axis, to define a point in a two-dimensional space. The x-axis is a horizontal line, and the y-axis is a vertical line that intersect at the origin (0, 0).
Understanding the Axes
The x-axis is used to measure the horizontal distance of a point from the origin, and the y-axis is used to measure the vertical distance of a point from the origin. The distance of a point from the origin is called its coordinates. It is denoted by (x, y). The x-coordinate is the horizontal distance from the origin, and the y-coordinate is the vertical distance from the origin.
- To plot a point in the Cartesian coordinate system, we start at the origin.
- After that move horizontally to the right if the x-coordinate is positive or to the left if the x-coordinate is negative.
- Then we move vertically up if the y-coordinate is positive or down if the y-coordinate is negative until we reach the point.
The Distance Formula
The distance between two points in the Cartesian coordinate system can be found using the distance formula, which is:
d = sqrt[(x2 – x1)^2 + (y2 – y1)^2]
where (x1, y1) and (x2, y2) are the coordinates of the two points.
The following topic would be helpful in better understanding of the cartesian coordinate system.