91Ó°ÊÓ

In the context of a Cartesian plane, ordered pairs are crucial. An ordered pair is a set of values written in a specific order, typically written as \( x, y \). It represents a point in a two-dimensional space where:

• The first number (x-coordinate) indicates the position along the horizontal axis.
• The second number (y-coordinate) represents the position along the vertical axis.

Ordered pairs, such as \( P(-\frac{1}{2}, 3) \), tell us exactly where to locate a specific point. For example, the ordered pair \( (-\frac{1}{2}, 3) \) tells us to move \( -\frac{1}{2} \) units left (since it's negative) and then 3 units up.
Always remember:

• \textbf{x-coordinate}: Position on the horizontal axis.
• \textbf{y-coordinate}: Position on the vertical axis.

Understanding ordered pairs is the first step in mastering graphing points on a Cartesian plane.

The Cartesian coordinates system is a method of representing points in a two-dimensional space using two numerical values. These values are known as coordinates and are written in an ordered pair format \( (x, y) \).
Here's how Cartesian coordinates work:

• \textbf{x-axis}: This is the horizontal line that runs left to right and is used to locate the \textbf{x-coordinate} of a point.
• \textbf{y-axis}: This is the vertical line that runs up and down and is used to locate the \textbf{y-coordinate} of a point.

The point where both the x-axis and y-axis intersect is known as the origin, denoted by \( (0, 0) \).
To locate a point on the Cartesian plane, refer to the ordered pair. For example, for the point \( S(2, -\frac{7}{3}) \), 2 is the \textbf{x-coordinate}, and \( -\frac{7}{3} \) is the \textbf{y-coordinate}. Move 2 units to the right on the x-axis and \( -\frac{7}{3} \) units down on the y-axis to plot this point.
Mastering Cartesian coordinates is key to accurately plotting points.

Graphing points on a Cartesian plane requires accurate interpretation of ordered pairs and their respective coordinates. Here are the steps:

• Identify the x-coordinate and y-coordinate from the ordered pair.
• Locate the x-coordinate on the horizontal axis.
• Locate the y-coordinate on the vertical axis.
• Where these two positions intersect is where you plot the point.

For instance, let's take Point P with coordinates \( P(-\frac{1}{2}, 3) \):

• Identify the coordinates: \( -\frac{1}{2} \) for x and 3 for y.
• Move \( -\frac{1}{2} \) units left on the x-axis.
• Move 3 units up on the y-axis.

This intersection is the location of Point P.
Similarly, plot Points Q, R, and S using the method above:

• Point Q (\( \frac{7}{2}, 4 \)): Move \( \frac{7}{2} \) or 3.5 units right and 4 units up.
• Point R (\( -3, -\frac{3}{4} \)): Move 3 units left and \( -\frac{3}{4} \) units down.
• Point S (2, \( -\frac{7}{3} \)): Move 2 units right and \( -\frac{7}{3} \) or approximately -2.33 units down.

Verifying the points after plotting helps ensure accuracy.