Grade 8
  1. Number Systems  1.1. Rational Numbers  1.2. Irrational Numbers  1.3. Real Numbers  1.4. Properties of Real Numbers  1.4.1. Commutative Property  1.4.2. Associative Property  1.4.3. Distributive Property  1.5. Representation on the Number Line  1.6. Operations on Real Numbers  1.6.1. Addition and Subtraction  1.6.2. Multiplication and Division  1.7. Rationalization  1.8. Exponents and Powers  1.9. Square Roots and Cube Roots
  2. Algebra  2.1. Algebraic Expressions  2.2. Identities and Simplification  2.2.1. Multiplying Binomials  2.2.2. Using Algebraic Identities  2.3. Factorization  2.3.1. Common Factors  2.3.2. Factorization by Grouping  2.3.3. Factorization of Trinomials  2.3.4. Special Products  2.4. Linear Equations in One Variable  2.4.1. Solving Linear Equations  2.4.2. Word Problems on Linear Equations
  3. Geometry  3.1. Understanding Quadrilaterals  3.1.1. Properties of Quadrilaterals  3.1.2. Types of Quadrilaterals  3.1.2.1. Parallelogram  3.1.2.2. Rectangle  3.1.2.3. Square  3.1.2.4. Rhombus  3.1.2.5. Trapezium  3.2. Constructions  3.2.1. Constructing Quadrilaterals  3.2.2. Constructing Bisectors  3.2.3. Constructing Angles  3.2.4. Constructing Triangles  3.3. Symmetry and Transformations  3.3.1. Reflection  3.3.2. Rotation  3.3.3. Translation  3.3.4. Symmetry in Patterns
  4. Mensuration  4.1. Area and Perimeter  4.1.1. Perimeter of Polygons  4.1.2. Area of Triangles  4.1.3. Area of Quadrilaterals  4.1.4. Area of Circles  4.2. Surface Area and Volume  4.2.1. Cubes  4.2.2. Cuboids  4.2.3. Cylinders  4.2.4. Cones  4.2.5. Spheres
  5. Data Handling  5.1. Organizing Data  5.2. Frequency Distribution Tables  5.3. Graphical Representation of Data  5.3.1. Bar Graphs  5.3.2. Histograms  5.3.3. Pie Charts  5.3.4. Line Graphs (added)  5.4. Probability  5.4.1. Introduction to Probability  5.4.2. Experimental Probability
  6. Coordinate Geometry  6.1. Cartesian Plane  6.2. Plotting Points  6.3. Coordinate System  6.4. Distance Between Points  6.5. Applications of Coordinate Geometry
  7. Introduction to Graphs  7.1. Linear Graphs  7.2. Applications of Graphs  7.3. Distance-Time Graphs  7.4. Speed-Time Graphs
  8. Comparing Quantities  8.1. Ratio and Proportion  8.2. Percentage  8.2.1. Increase and Decrease Percent  8.2.2. Discount in Percentage  8.2.3. Profit and Loss in Percentage  8.2.4. Simple Interest  8.2.5. Compound Interest
  9. Exponents and Powers  9.1. Laws of Exponents  9.2. Negative Exponents  9.3. Standard Form  9.4. Applications of Exponents
  10. Introduction to Squares and Square Roots  10.1. Properties of Square Numbers  10.2. Finding Square Roots  10.2.1. Prime Factorization Method  10.2.2. Division Method  10.3. Estimating Square Roots
  11. Introduction to Cubes and Cube Roots  11.1. Properties of Cube Numbers  11.2. Finding Cube Roots  11.2.1. Prime Factorization Method in Finding Cube Roots

Grade 8 → Coordinate Geometry ↓


Coordinate System


The coordinate system is a fundamental concept in mathematics that allows us to represent and analyze geometric shapes and their relationships. It serves as a bridge between algebra and geometry, allowing us to solve problems in both fields from a unified perspective. The coordinate system was developed by French mathematician René Descartes, which is why it is often referred to as the Cartesian coordinate system.

What is a coordinate system?

A coordinate system is a method of using numbers to represent a point, line, or any geometric feature in space. The most common type of coordinate system is the two-dimensional Cartesian coordinate system. In this system, any point in the plane is determined by two numbers called coordinates. These coordinates are usually written as pairs in the form (x, y).

Understanding the Cartesian coordinate system

The Cartesian coordinate system has two perpendicular lines, called axes, that intersect at the origin. The horizontal axis is often called the x-axis, and the vertical axis is called the y-axis. The origin is (0, 0).

Y X (0,0)

The position of any point is determined by its distance from two axes. The first number, x, represents the horizontal distance along the x-axis, and the second number, y, represents the vertical distance along the y-axis.

Quadrants of the Cartesian plane

The two axes divide the plane into four regions, called quadrants. They are numbered in a counterclockwise direction starting from the top right. Each quadrant represents a different combination of signs for x and y.

Quadrant I (+,+) Quadrant II (-,+) Quadrant III (-,-) Fourth Quadrant (+,-)

Drawing of points in a coordinate system

To plot a point in a coordinate system, you need its coordinates (x, y) Start at the origin:

  • Move horizontally along the x-axis to position x.
  • From there, move vertically to position y.

Where you stop is the position of the point (x, y).

Example

Let us plot the point (3, 4).

  • Starting at the origin, move 3 units to the right along the x-axis.
  • Move up 4 units from this new position.

Here the point (3, 4) is found.

(3, 4)

The role of the coordinate system in geometry

The coordinate system allows us to study geometric shapes by transforming geometric problems into algebraic equations. This transformation makes it possible to apply algebraic methods to solve geometric problems.

Lines in the coordinate plane

A line in the coordinate plane can be represented by the following equation:

y = mx + c

where m is the slope of the line, and c is the intercept on the y-axis.

Examples: draw a line

Consider the equation of the line y = 2x + 1.

  • The slope m = 2 means that the line rises two units for every one unit moved to the right.
  • The y-intercept c = 1 means that the line intersects the y-axis at the point (0, 1).

Let us mark this line.

(0, 1)

As you can see, the line crosses the y-axis at (0, 1) and follows a slope while moving on the plane.

Applications and significance

Coordinate systems are widely used in various fields of science and engineering. It helps in visualization of concepts and accurate analysis of spatial relationships. Whether in navigation, computer graphics or robotics, understanding coordinate systems opens up a world of possibilities.

In short, the coordinate system is a universal mathematical tool that helps us put numbers on geometry, thus providing a precise and consistent way to describe and analyze spatial patterns and relationships. It provides a way to think about space and time in a mathematical sense and is a fundamental aspect of many scientific advances.


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Coordinate System

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