How to plot points in the rectangular coordinate plane? - The Cartesian Coordinate System

Hi everyone, today's post is about "How to plot points in the rectangular coordinate plane?" As we all know a firm grasp on this concept and its application is necessary to help us progress smoothly to more advanced topics in Algebra.

In order to meet our target, one should have a clear understanding on the following key terms:

The rectangular coordinate plane also called the Cartesian coordinate system in honor of the French mathematician René Descartes, is formed by two real number lines, called axes, that are drawn perpendicular to each other. The horizontal number line is called the x-axis, while the vertical number line is called the y-axis. These two axes intersect at a point called the origin, and divide the plane into four regions called quadrants.

In Illustration:

Note to ponder:

• Every point in the coordinate plane has one-to-one correspondence with set of coordinate pairs (x,y)
• The first number in the ordered pair, called the x-coordinate or abscissa is the horizontal distance of a point from the y-axis.
• The second number, called the y-coordinate or ordinate is the vertical distance of a point from the x-axis
• The ordered pair (x,y) is called the coordinates of the point in the rectangular coordinate plane

How to plot or graph a point (x,y) in the coordinate plane?

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Steps:

1. Start at the origin (0,0)
2. Go "x" units to the right if "x" is positive or "x" units to the left if "x" is negative.
3. Go "y" units up if "y" is positive or "y" units down if "y" is negative.

Example 1.1:

Plot the points A(3, -2) and B(-3,2) in the Cartesian Plane.

A(3, -2)

1. Start at the origin (0,0)
   

1. Go 3 units to the right since "x" is positive
   

1. Go 2 units down since "y" is negative
   

For B(-3, 2)

1. Start at the origin (0,0)
   

1. Go 3 units to the left since "x" is negative
   

1. Go 2 units up since "y" is positive
   

Summary of the steps:

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Plot the points A(3, -2) and B(-3,2) in the Cartesian Plane.

Additional input: How to determine the coordinates of a point in the plane?

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To determine the coordinates of a point in a plane, reverse the procedure.

Example 1.2

Give the coordinates of each given point on the graph.

Now, you might feel how easy this is. Yes, it is very easy to do and you will not find any difficulties while doing it.
Have a nice day!

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references:

1. https://en.wikipedia.org/wiki/Cartesian_coordinate_system
2. Advanced Algebra and Trigonometry Textbook