Cartesian Plane

 

The Cartesian plane consists of two directed lines that perpendicularly intersect their respective zero points.

 

From the figure below, you can understand that

  • The horizontal directed line is called the x-axis and the vertical directed line is called the y-axis.
  • The point of intersection of the x-axis and the y-axis is called the origin and is denoted by the letter O.

The Coordinates

  • The position of any point on the Cartesian plane is described by using two numbers: (x, y). 
  • The first number, x, is the horizontal position of the point from the origin. It is called the x-coordinate.
  • The second number, y, is the vertical position of the point from the origin. It is called the y-coordinate
  • Since a specific order is used to represent the coordinates, they are called ordered pairs.

Let us consider the following example:

The ordered pair (5, 8) represents a point 5 units to the right of the origin in the direction of the x-axis and 8 units above the origin in the direction of the y-axis as shown in the diagram below.

The x-coordinate of point P is 5; and the y-coordinate of point P is 8.

(i.e.) The coordinates of point P are (5, 8).

  • For the point P(5, 8), the ordered pair is (5, 8). 

So: 5 is the x-coordinate, and 8 is the y-coordinate.

  • P(5, 8) means P is 5 units to the right of and 8 units above the origin.

Example Question:

State the coordinates of each of the points shown on the Cartesian plane:

Answer:

A is 3 units to the right of and 2 units above the origin. So, point A is (3, 2).
B is 5 units to the right of and 5 units above the origin. So, point B is (5, 5).
C is 7 units to the right of and 8 units above the origin. So, point C is (7, 8).
D is 6 units to the left of and 4 units above the origin. So, point D is (–6, 4).
E is 3 units to the left of and 7 units above the origin. So, point E is (–3, 7).
F is 4 units to the left of and 6 units below the origin. So, point F is (–4, –6).
G is 8 units to the left of and 8 units below the origin. So, point G is (–8, –8).
P is 9 units to the right of and 9 units below the origin. So, point P is (9, –9).
Q is 6 units to the right of and 5 units below the origin. So, point Q is (6, –5).