Quadrants and axes

Key Notes :

1. Introduction to the Coordinate Plane

• Coordinate Plane: A two-dimensional plane formed by the intersection of two perpendicular number lines called the x-axis (horizontal) and y-axis (vertical).
• Axes:
  • X-Axis: The horizontal axis.
  • Y-Axis: The vertical axis.
• Origin: The point of intersection of the x-axis and y-axis, denoted as (0, 0).

2. Understanding Coordinates

• Ordered Pairs: Coordinates are written as ordered pairs (x, y), where ‘x’ is the position on the x-axis and ‘y’ is the position on the y-axis.
  • Example: (3, 4) means moving 3 units along the x-axis and 4 units up the y-axis.

3. The Four Quadrants

The coordinate plane is divided into four quadrants:

• First Quadrant:
  • Location: Top-right section.
  • Sign of Coordinates: Both x and y are positive (x > 0, y > 0).
  • Example: (2, 5).

• Second Quadrant:
  • Location: Top-left section.
  • Sign of Coordinates: x is negative, y is positive (x < 0, y > 0).
  • Example: (-3, 4).

• Third Quadrant:
  • Location: Bottom-left section.
  • Sign of Coordinates: Both x and y are negative (x < 0, y < 0).
  • Example: (-4, -6).

• Fourth Quadrant:
  • Location: Bottom-right section.
  • Sign of Coordinates: x is positive, y is negative (x > 0, y < 0).
  • Example: (5, -7).

4. Axes and Points on Axes

• Points on the X-Axis:
  • Have coordinates of the form (x, 0), meaning they lie directly on the x-axis.
  • Example: (3, 0) lies 3 units to the right of the origin.

• Points on the Y-Axis:
  • Have coordinates of the form (0, y), meaning they lie directly on the y-axis.
  • Example: (0, -2) lies 2 units below the origin.

5. Plotting Points

• Steps to Plot a Point:
  1. Start at the origin (0, 0).
  2. Move horizontally along the x-axis according to the x-coordinate.
  3. Move vertically along the y-axis according to the y-coordinate.
  4. Mark the point where these positions intersect.

6. Examples

• Example 1: Plot the point (4, 3).
  • Move 4 units right along the x-axis and 3 units up along the y-axis.
  • The point lies in the first quadrant.

• Example 2: Plot the point (-2, -5).
  • Move 2 units left along the x-axis and 5 units down along the y-axis.
  • The point lies in the third quadrant.

7. Significance of Quadrants

• Symmetry: Understanding the quadrants helps in identifying the symmetry of points with respect to the axes and origin.
• Graphing Functions: Quadrants are used to graph linear and non-linear functions, understanding the behavior of the graph in different quadrants.
• Real-Life Applications: Used in mapping, physics (vector representation), economics (demand and supply analysis), and many other fields.

8. Common Mistakes to Avoid

• Confusing Signs: Misinterpreting the signs of the coordinates can place points in the wrong quadrant.
• Origin Misplacement: Failing to start plotting from the origin can lead to incorrect positioning of points.
• Axes Mix-Up: Confusing the x and y coordinates can lead to incorrect graphing.

Learn with an example

Let’s practice!