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.
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.
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?
Solution:
In this, we plot the points A (3, 4), B (−3, 2), C (−4, 4), D (5, −3), and E (−2, −2) on the coordinate plane. Point A lies in the first quadrant, points B and C lie in the second quadrant, point E lies in the third quadrant, and point D lies in the fourth quadrant.
a) C is come in second quadrant, E is come in III quadrant and D is come in IV quadrant. b) Here A is come in first quadrant and D is come in IV quadrant.
