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Coordinate Plane

This page is based on co-ordinate plane and graphing coordinates. First let's understand what is a coordinate plane. The XY plane or Cartesian plane or the coordinate plane is a plane whose points are identified with ordered pairs of real numbers. Each point (say P) on the XY plane is determined by an X-coordinate and a Y-coordinate. The X-coordinate specifies horizontal position of P and the Y-coordinate specifies the vertical position. The XY plane is main setting for two-dimensional analytic geometry. In higher mathematics, the xy plane is usually identified with the set $R^{2}$ consisting of all ordered pairs of real numbers. The example of XY plane is shown below,

Coordinate Plane
Let us go ahead and learn about the coordinate plane in detail.

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Definition

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The coordinate plane is also known as Cartesian plane or Cartesian coordinate plane. It is the two-dimensional form of Cartesian system. Coordinate plane is defined as a plane which is made up of two perpendicular axes; horizontal one is called X-axis, while vertical is known as Y-axis. The numbers are notified on these axes. The intersection point of these axes denotes zero, called origin (0, 0). The coordinate plane is used to represent the position of a a point or an object in terms of coordinates. Each point is specified by the distance from the origin. This distance is written in the form of coordinates which is an ordered pair of numbers. Have a look at the following image :

Definition of Coordinate Plane

When we move right side of origin on the X axis, we find positive numbers and on left side of zero, there are negative numbers. Similarly, on Y axis, there are positive number in upward direction and negative numbers in downward direction. Thus, a coordinate plane is divided into four quadrants as shown above.

Therefore, we can say that -
(i) A point with positive x coordinate and positive y coordinate (i.e. (x, y)) falls in first quadrant.
(ii) A point with negative x coordinate and positive y coordinate (i.e. (-x, y)) falls in second quadrant.
(iii) A point with negative x coordinate and negative y coordinate (i.e. (-x, -y)) falls in third quadrant.
(iv) A point with positive x coordinate and negative y coordinate (i.e. (x, -y
)) falls in fourth quadrant.

Blank Coordinate Plane

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A blank coordinate plane looks like the image below.

Blank Coordinate Plane

There is origin at the intersection. It is usually denoted by O whose coordinates are (0, 0). The X axis and Y axis pass through the origin horizontally and vertically. The number written on these axis increase on the right side as well in upward direction, while they decrease on the left side and in downward direction of the origin.

Plotting Points on Coordinate Plane

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While plotting points on coordinate plane, following steps are to be followed.

Step 1 : First check in which quadrant our given point lies, using information given in above section.
Step 2 : Move given units on X axis. For example, if x-coordinate is -3, then one should move 3 units to the negative side of X axis.
Step 3 : From this point, move given units parallel to Y axis. For example, if y-coordinate is given as 6, then from point obtained in                   previous step, move parallel to Y axis till 6 units.
Step 4 : Now, place a point at this position and name it.
Step 5 : Cross check whether it is situated in the right quadrant determined in step 1. For example - point (-3, 7) will lie in second                     quadrant.

Examples

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Have a look at the following example of plotting points on coordinate plane.

Example 1 : Plot following points in coordinate plane :
(4, 5) and (-3, 1)

Solution : These points are shown below.

Examples on Coordinate Plane

Example 
2 : Graph (-4, -3), (-2, 2) and (1, -6)

Solution : Required graph is -

Coordinate Plane Examples

Example 3 : Plot the point 
(1.5, -2.5), (4.5, 0.5) and (-6, -5) on coordinate plane.

Solution : The required points are shown below :

Coordinate Plane Graph
More topics in Coordinate Plane
Axes Coplanar Points
Equidistant Points Equidistant Planes
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