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 ↓


Plotting Points


Coordinate geometry, also known as Cartesian geometry, is a branch of mathematics that uses numbers and algebraic expressions to define points in the plane. The concept is named after René Descartes, who introduced the idea of describing the position of points using ordered pairs of numbers (coordinates). In Class 8 Maths, an essential topic is to understand how to plot points on a coordinate plane.

Understanding the coordinate plane

The coordinate plane is a two-dimensional surface where we can draw points, lines, and curves. It consists of two perpendicular lines, the x-axis and the y-axis, which intersect at a point called the origin. The x-axis is the horizontal line, while the y-axis is the vertical line.

    y-axis |  
           ,  
           ,  
           ,  
    -------+-------> x-axis
           ,  
           ,  
           ,  
           ,

Produce

The origin is the point where the x-axis and y-axis intersect. It is represented by the coordinates (0, 0). In this context, 0 represents a position on both the x-axis and the y-axis.

    Origin coordinates: (0, 0)

Quadrant

The coordinate plane is divided into four regions, known as quadrants. Each quadrant is defined by the signs of the x and y coordinates of the points that lie within them:

  • Quadrant I: (+, +)
  • Quadrant II: (−, +)
  • Quadrant III: (−, −)
  • Fourth Quadrant: (+, −)
    y-axis ^
          , Quadrant II Quadrant I
          | (, +) | (+, +)
    ------+--------------+-------> x-axis
          , Quadrant III Quadrant IV
          | ()

Plotting points

To plot points on the coordinate plane, we need to understand the structure of an ordered pair. An ordered pair is written as (x, y), where x is the x-coordinate and y is the y-coordinate. The x-coordinate indicates how far the point is on the horizontal axis, while the y-coordinate shows its position on the vertical axis.

Steps to mark a point

  1. Start at the origin (0, 0).
  2. Move horizontally to the x-coordinate:
    • If x is positive, move to the right.
    • If x is negative, move to the left.
  3. Walk perpendicular to the y-coordinate:
    • If y is positive, go up.
    • If y is negative, go down.
  4. Mark the spot where you will land.

Example 1: Plotting the point (3, 4)

Let us plot the point (3, 4) step by step.

  1. Start at the origin (0, 0).
  2. Move 3 units to the right (positive x-direction).
  3. Move up 4 units (positive y-direction).
  4. Mark a point at this location.

The point (3, 4) is in quadrant I because both the x-coordinate and y-coordinate are positive.

    Plot of point (3, 4)

    y-axis ^
          | . (3, 4)
          ,
          ,
    ------+--------------+-------> x-axis
          ,
          ,
          ,

Example 2: Plotting the point (-2, 5)

Let us plot the point (-2, 5).

  1. Start at the origin (0, 0).
  2. Move 2 units to the left (negative x-direction).
  3. Move up 5 units (positive y-direction).
  4. Mark a point at this location.

The point (-2, 5) is in quadrant II because the x-coordinate is negative and the y-coordinate is positive.

    Plot of the point (-2, 5)

    y-axis ^
          ,   
          | . (-2, 5)
          ,      
    ------+--------------+-------> x-axis
          ,
          ,
          ,

More complex examples

Let's try a few more points with different signs and values:

Point Description
(-4, -3) Start at (0, 0). Move 4 units to the left and 3 units down. This is in quadrant III.
(0, 2) Start at (0, 0) and move up 2 units. This lies on the y-axis.
(5, -1) Start at (0, 0). Move 5 to the right and 1 down. This is in quadrant IV. 
    Example plot:

    y-axis ^
          ,                
          | . (0, 2)
          ,            
      .(-4, -3)---------+-------> x-axis
          | . (5, -1)
          ,
          ,

Importance of plotting points

Plotting points is fundamental to understanding more advanced concepts in coordinate geometry. This skill forms the basis for graphing equations, analyzing geometric shapes, and understanding algebra more deeply. By looking at points on the coordinate plane, students develop an intuitive understanding of the differences between algebra and geometry.

Practice problems

To become more familiar with point drawing, try these practice problems:

  1. Mark the point (7, -3) and state its position.
  2. Find and plot the point directly opposite to (2, -5) in the coordinate plane.
  3. Plot the points (0, 0), (4, 0) and (4, 3). What shape do these points form?

Regularly practicing such problems can provide a solid foundation in coordinate geometry, which is important for tackling more complex mathematical challenges in higher classes.


Grade 8 → 6.2


U
username
0%
completed in Grade 8

← Prev (6.1)
Cartesian Plane
Next (6.3) →
Coordinate System

Comments 



Plotting Points

https://www.buddymath.com/g8/6.2?bmal=en