91Ó°ÊÓ

The coordinate plane is a two-dimensional surface where we can position points using two numbers, known as coordinates. These numbers represent the distance of the point from two perpendicular lines called axes. Typically, the axes are labeled as the x-axis (horizontal) and y-axis (vertical).
The coordinate plane is a fundamental concept in coordinate geometry, enabling us to visualize algebraic equations, locate positions, and understand spatial relationships. Any point on this plane is denoted by an ordered pair of numbers \(x, y\), which indicate its displacement from the coordinate axes.

• **X-Axis**: Runs horizontally and determines the first value in the coordinate pair.
• **Y-Axis**: Runs vertically and determines the second value in the coordinate pair.

The intersection of these axes is the origin, the most crucial point, as all other points are located in relation to it.

The origin point is a central concept in the coordinate plane. It serves as the reference point from which all coordinate measurements begin. By definition, it is where the x-axis and y-axis intersect.
The coordinates of the origin are always \(0, 0\). This means that the origin is situated at zero distance along both the x and y axes from itself. The origin provides a reference for measuring how far and in which direction other points lie on the coordinate plane.

• **Starting Point**: Every movement on the coordinate plane is usually measured starting from the origin.
• **Center of Coordinates**: It divides the coordinate plane into four quadrants.

The origin being \(0, 0\) allows students to easily understand how to calculate other points in relation to it.

Movement along the x-axis affects only the x-coordinate of a point, while the y-coordinate remains unchanged.
When you start from the origin (0,0) and move along the x-axis by a certain distance, you modify the first number in the coordinate pair:

• **Positive Direction**: Moving right increases the x-coordinate.
• **Negative Direction**: Moving left decreases the x-coordinate.

For instance, moving 4 units positively from the origin changes the coordinates from \(0, 0\) to \(4, 0\). Note how only the x-coordinate changes, illustrating that movement along the x-axis specifically alters the horizontal position of a point on the plane.

Y-axis movement refers to changes in a point's position vertically on the coordinate plane. This affects only the y-coordinate, leaving the x-coordinate unchanged.
In our exercise, after moving along the x-axis, the point was \(4, 0\).

• **Positive Direction**: Moving upward increases the y-coordinate.
• **Negative Direction**: Moving downward decreases the y-coordinate.

For example, moving downward by 3 units from \(4, 0\) transforms the coordinates to \(4, -3\), indicating a change in the vertical positioning. The final movement highlights that any adjustments along the y-axis only impact the vertical coordinate.