Coordinate Plane (original) (raw)

Last Updated : 21 Apr, 2026

The coordinate plane, also known as the Cartesian plane, is a two-dimensional plane formed by the intersection of two perpendicular number lines, typically referred to as the x-axis and y-axis.

co-plane

The x-axis and y-axis meet at a point called the origin, written as (0, 0).
Each point on the coordinate plane represents an ordered pair of real numbers called coordinates.
The x-coordinate indicates how far to travel horizontally from the origin (right if positive and left if negative).
The y-coordinate indicates how far to move vertically (up if positive, downward if negative).

Coordinate Plane Quadrants

Quadrants are the four regions of the coordinate plane created by the x-axis and y-axis. Each quadrant has different sign conventions and is represented by Roman numerals I, II, III, and IV.

**Quadrant I: Quadrant I is located in the upper right. Quadrant I has positive values on both the x-axis and y-axis.
**Quadrant II: Quadrant II is located in the upper left, has negative numbers on the x-axis, and has positive numbers on the y-axis.
**Quadrant III: Quadrant III is located at the bottom left. Quadrant III has negative values on both the x-axis and y-axis.
**Quadrant IV: Quadrant IV is located in the bottom right corner. Quadrant IV has positive numbers on the x-axis and negative values on the y-axis.

Characteristics of a Coordinate Plane

There are various characteristics of the coordinate plane, such as:

The coordinate plane is made up of two perpendicular axes, termed the coordinate axes, which intersect at a point known as the origin.
A point's Cartesian coordinates may be calculated by measuring its distance from the origin along the x and y axes.
The coordinate plane exhibits various types of symmetry, such as reflection symmetry across the x-axis, y-axis, or origin, depending on the nature of the geometric figure or function being analysed.

Graphing on a Coordinate Plane

Let us learn how to build a graph step by step using the following points: (2, -6), (2, 2), and (-4, 3).

Point (2, -6): Move 2 units to the right on the x-axis and 6 units down on the y-axis. This point lies in Quadrant IV.
Point (2, 2): Move 2 units to the right on the x-axis and 2 units up on the y-axis. This point lies in Quadrant I.
Point (-4, 3): Move 4 units to the left on the x-axis and 3 units up on the y-axis. This point lies in Quadrant II.

After plotting these points, join them with straight lines as shown in the graph.

Coordinate Geometry

Quadrants

Area of Quadrant

Distance Between Two Points Formula

3D Distance Formula

Solved Examples

**Example 1: Plot the following points on a Coordinate plane:

A (-4, 2), B (4, 4), C (5, -2), D (5, 2)

**Solution:

In this, we plot the points A (−4, 2), B (4, 4), C (5, −2), and D (5, 2) on the coordinate plane. Point A lies in the second quadrant, points B and D lie in the first quadrant, and point C lies in the fourth quadrant.

**Example 2: Here are some points plotted on a coordinate plane. A (3, 4), B (-3, 2), C (-4, 4), D (5, -3), E (-2, -2). Look at the points on the graph below and answer the following questions:

a) Which quadrants contain the points C, D, and E?
b) Which points are in either the first or fourth quadrant?