91Ó°ÊÓ

Have you ever wondered how we determine the position of points in a plane? The Cartesian Coordinate System is a mathematical structure that helps us do just that. It consists of two number lines that intersect at a right angle. One is horizontal, called the x-axis. The other is vertical, known as the y-axis.
This intersection point is the origin, marked as (0,0). From here, the Cartesian plane is divided into four sections. These sections are known as quadrants. They are labeled counter-clockwise: Quadrant I (where both x and y are positive), Quadrant II (where x is negative and y is positive), Quadrant III (where both x and y are negative), and Quadrant IV (where x is positive and y is negative).

• Quadrant I: (+x, +y)
• Quadrant II: (-x, +y)
• Quadrant III: (-x, -y)
• Quadrant IV: (+x, -y)

Understanding this helps us pinpoint where a particular set of coordinates lies in the plane.

When we talk about the x-coordinate, we are referring to the horizontal position of a point. In the Cartesian coordinate system, the x-axis runs left to right across the plane. The x-coordinate tells us how far left or right the point is from the origin. A positive x-coordinate indicates the point is to the right of the origin, while a negative x-coordinate means it is to the left.
Let's say we have the point (1, 2), for example. The number 1 is the x-coordinate. Since 1 is greater than zero, it tells us that the point is one unit to the right of the origin.
To determine which quadrant a point is in, you start by checking the sign of the x-coordinate. This is your first clue in quadrant identification.

The y-coordinate represents a point's vertical position in the Cartesian plane. This is determined by the y-axis, which runs up and down. A positive y-coordinate places the point above the origin, and a negative value places it below.
Take the point (1, √3) as an example. Here, √3 approximates to 1.732, which is positive. This tells us that the point is just over 1.7 units above the origin.
Identifying the sign of the y-coordinate is the second step when figuring out which quadrant a point belongs to. For instance, if both the x-coordinate and y-coordinate are positive, as in our example of (1, √3), the point is in Quadrant I. This pattern applies as you extend this logic to all other quadrants.