Coordinate Plane

French mathematician Rene Descartes developed the coordinate plane in the 17th century to show how algebra can be used to solve various geometric problems. The coordinate plane can be defined as a system with a horizontal line (x-axis) and a vertical line (y-axis) intersecting at right angles. These lines are called axes. The intersection of these perpendicular lines is called the origin. The origin is marked as zero. The horizontal and vertical lines are marked with integers following the number line. 

Properties of a Coordinate Plane

• The coordinate plane consists of two perpendicular axes and an intersection as the origin. The axes are also called the coordinate axes.
• These are used to mark the integer numbers as per the user’s measurements and are used to plot graphs or geometrical structures on the plane. 
• This plane is two-dimensional. 
• The coordinate plane is also called the Cartesian plane in honour of the inventor of this plane, Descartes. 

Quadrants in a Coordinate Plane

As per the definition of the coordinate axis, the perpendicular axes divide the plane into 4 equal parts that are called quadrants. These quadrants contain both positive and negative numbers. They are: 

• Quadrant I: Both x- and y-coordinates are positive.
• Quadrant II: X-coordinates are negative, and y-coordinates are positive.
• Quadrant III: Both x- and y-coordinates are negative.
• Quadrant IV: X-coordinates are positive, and y-coordinates are negative.

Signs and Symbols Associated with Quadrants:

• The axes consist of positive and negative sides. 
• The right side of the x-axis is said to be the plane’s positive x-axis, and the left side is denoted as the negative axis.
• Similarly, on the y-axis, the upper part of the axis is the positive axis, and the lower y-axis is the negative y-axis. 
• The quadrants and the positive and negative axis play a major role in plotting graphs in trigonometry. They decide the nature of the graph according to the quadrant it falls into.
• The value of x is also called the abscissa or the x-coordinate. It indicates the distance of the point from the y-axis and the origin. 
• The value of y is called the ordinate or the y-coordinate. It indicates the distance of the point from the x-axis and the origin.

How to Plot a Point on the Coordinate Plane

To find the location of a point on a graph, we use x- and y-coordinates. These coordinates are called an ordered pair. They are written in curved brackets, separated by a comma in between.

For example, (5,8) is an ordered pair. The first number, 5, denotes the x-coordinate, whereas 8 is the y-coordinate. The x-coordinate is always the first number to be plotted on a graph.

Here are the steps for plotting a graph in a coordinate plane:

• The first number written in an ordered pair is the x-coordinate, and the latter is the y-coordinate. So to plot that point in the plane, we need to first locate the x-coordinate. 
• Move up as many units as the number from the x-axis to plot the abscissa. 
• Similarly, move as many units mentioned in the ordered pair from the y-axis to plot the ordinate. 
• We also need to consider the signs of the numbers in the ordered pair. 

By following these steps, the particular point will be plotted in the coordinate plane. Once we have the required ordered pairs, we can easily plot a graph or find a point in a map. In survey maps, these coordinate planes can be used to plot a particular point, such as a monument or landmark.

Conclusion

This article covered the basics of Cartesian planes and how they affect geometry. It also explained how to plot a point in a two-dimensional coordinate plane. This way, one can plot trigonometric graphs. 

Coordinate planes are also used to find the domain and range of any linear equation by plotting the line on the plane. These graphs are also helpful in plotting bar graphs in statistics. Moreover, the straight lines in these graphs can be used to find the slopes or mirror images of the lines.