E CONTENT

 Name: COORDINATES

Learning Outcomes

After studying this chapter, students will be able to:

• Understand the concept of a coordinate plane.
• Identify the x-axis, y-axis, and origin.
• Understand the meaning of an ordered pair (x, y).
• Locate and identify points on the coordinate plane.
• Determine the coordinates of a given point from a graph.
• Recognize the four quadrants of the coordinate plane.
• Apply the concept of coordinates in real-life situations such as maps and navigation.

Introduction

Coordinates are an important concept in coordinate geometry, which links algebra with geometry. They help us identify the exact position of a point on a plane using numbers. The system used for locating points is called the Cartesian Coordinate System, developed by the mathematician René Descartes.

In this system, two perpendicular number lines intersect to form a plane:

• The x-axis (horizontal axis)
• The y-axis (vertical axis)

The point where both axes intersect is called the origin (0,0). By measuring the distances from these axes, we can determine the coordinates of any point on the graph.

The Coordinate Plane

A coordinate plane is formed when two number lines intersect at right angles.

• X-axis – the horizontal number line
• Y axis – the vertical number line
• Origin-(0,0) – the point where both axes meet

The coordinate plane is divided into four regions called quadrants:

• Quadrant I: x positive, y positive
• Quadrant II: x negative, y positive
• Quadrant III: x negative, y negative
• Quadrant IV: x positive, y negative 

Coordinates of a Point

• The position of a point on a graph is represented by an ordered pair (x, y).
• x- coordinate – the horizontal distance from the y-axis
• y-coordinate – the vertical distance from the x-axis

Example:

For the point (4,3)

• Move 4 units to the right along the x-axis
• Move 3 units upward along the y-axis
• This determines the exact location of the point.

Steps to Find the Coordinates of a Point

1. Locate the point on the graph.
2. Move vertically down or up to the x-axis to determine the x-value.
3. Move horizontally left or right to the y-axis to determine the y-value.
4. Write the coordinates as an ordered pair (x, y).

 Example

If a point A lies:

3 units to the right of the origin

2 units above the x-axis

Then the coordinates of point A = (3,2).

Practical Applications of Coordinates

The concept of coordinates is used in many real-life situations:

1. Maps and GPS Navigation

Coordinates help determine exact locations on maps and are used in global positioning systems (GPS).

2. Computer Graphics

In computer games and animations, coordinates determine the position of images and objects on the screen.

3. Architecture and Engineering

Engineers use coordinate systems to design buildings, roads, and bridges accurately.

4. Astronomy

Astronomers use coordinates to locate stars, planets, and other celestial objects in space.

5. Robotics

Robots move and perform tasks using coordinate positions programmed into their systems.

Conclusion

Coordinates provide a simple and effective way to locate points on a plane using numbers. By understanding the coordinate plane, axes, origin, and ordered pairs, students can easily determine the position of any point. The concept of coordinates is not only important in mathematics but is also widely used in technology, navigation, engineering, and science, making it an essential topic for practical and academic learning

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