Plotting Points on the Coordinate Plane
Learning Outcomes
- Define the components of the Cartesian coordinate system.
- Plot points on the Cartesian coordinate plane.
The Cartesian coordinate system with all four quadrants labeled.
Try It
[ohm_question]92752[/ohm_question] An illustration of how to plot the point (3,-1).
When dividing the axes into equally spaced increments, note that the x-axis may be considered separately from the y-axis. In other words, while the x-axis may be divided and labeled according to consecutive integers, the y-axis may be divided and labeled by increments of 2 or 10 or 100. In fact, the axes may represent other units such as years against the balance in a savings account or quantity against cost. Consider the rectangular coordinate system primarily as a method for showing the relationship between two quantities.
A General Note: Cartesian Coordinate System
A two-dimensional plane where the- x-axis is the horizontal axis
- y-axis is the vertical axis
Example: Plotting Points in a Rectangular Coordinate System
Plot the points [latex]\left(-2,4\right)[/latex], [latex]\left(3,3\right)[/latex], and [latex]\left(0,-3\right)[/latex] in the coordinate plane.Answer: To plot the point [latex]\left(-2,4\right)[/latex], begin at the origin. The x-coordinate is –2, so move two units to the left. The y-coordinate is 4, so then move four units up in the positive y direction. To plot the point [latex]\left(3,3\right)[/latex], begin again at the origin. The x-coordinate is 3, so move three units to the right. The y-coordinate is also 3, so move three units up in the positive y direction. To plot the point [latex]\left(0,-3\right)[/latex], begin again at the origin. The x-coordinate is 0. This tells us not to move in either direction along the x-axis. The y-coordinate is –3, so move three units down in the negative y direction.
Analysis of the Solution
Note that when either coordinate is zero, the point must be on an axis. If the x-coordinate is zero, the point is on the y-axis. If the y-coordinate is zero, the point is on the x-axis.Try It
[ohm_question]92753[/ohm_question]Try it
You can use an online graphing calculator to practice plotting points on the Cartesian Coordinate plane. Watch the following short video to learn how! https://youtu.be/eS6kabG2omI?list=PLfM6zMGnbgOGLZc-_Yj3QVK3Vz_L4Cw59 Now try plotting the following points with an online graphing calculator. [latex-display](4,0)[/latex-display] [latex-display](-1,5)[/latex-display] [latex-display](0,-10)[/latex-display] [latex-display](2,7)[/latex-display] [latex-display](3,-5)[/latex-display] [latex-display](-4,-7)[/latex-display]Licenses & Attributions
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- Revision and Adaptation. Provided by: Lumen Learning License: CC BY: Attribution.
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- College Algebra. Provided by: OpenStax Authored by: Abramson, Jay et al.. License: CC BY: Attribution. License terms: Download for free at http://cnx.org/contents/[email protected].
- Learn Desmos: Points. Authored by: Desmos. License: All Rights Reserved. License terms: Standard YouTube License.
- Question ID 92752, 92753. Authored by: Michael Jenck. License: CC BY: Attribution. License terms: IMathAS Community License, CC-BY + GPL.
CC licensed content, Specific attribution
- College Algebra. Provided by: OpenStax Authored by: OpenStax College Algebra. Located at: https://cnx.org/contents/[email protected]:1/Preface. License: CC BY: Attribution.