Plotting Points in Rectangular Coordinate System

An online graphing calculator to graph points in a rectangular coordinate system. Through these tutorials and interactive applets, you will be able to explore the properties of points and quadrants in Cartesian coordinate systems. If needed, free graph paper is available.

Definition of Rectangular Coordinate System

A rectangular coordinate system, or Cartesian plane, is a set of two intersecting and perpendicular axes forming an \( xy \)-plane. The horizontal axis is usually labeled the \( x \)-axis and the vertical axis is usually labeled the \( y \)-axis. The two axes divide the plane into four parts called quadrants. Any point on the plane corresponds to an ordered pair \((x, y)\) of real numbers \( x \) and \( y \), where \( x \) is called the \( x \)-coordinate and \( y \) is called the \( y \)-coordinate. Below is an applet that you may use to interactively explore points in a rectangular coordinate system.

Plot Points in Rectangular Coordinate System

Enter the \( x \)-coordinate and \( y \)-coordinate and click "Plot Point".

\( x = \)
\( y = \)

Hover your mouse cursor over the point to read coordinates, or use the Plotly toolbar in the top right of the graph to download the graph as a PNG file.

Tutorial 1 - Quadrants in Rectangular Coordinate System

For each point or ordered pair below, enter \( x \) and \( y \) into the calculator and plot the corresponding point. Determine the quadrant or axis where each point is located:

\((2, 3), \; (-2, -1), \; (0, -2), \; (2, -1), \; (0, 0), \; (-2, 3), \; (2, 0)\)
\((-2, 2), \; (0, 3), \; (1, -2), \; (2, 1), \; (-3, 0), \; (-2, -3), \; (2, -2)\)

Questions & Explorations

Question Part 1: Quadrant Signs & Axis Locations

Use the results in the above tutorial, and perhaps some other points, to answer the following questions:

  1. For what values of \( x \) and \( y \) is the point \((x, y)\) situated in Quadrant I?
  2. For what values of \( x \) and \( y \) is the point \((x, y)\) situated in Quadrant II?
  3. For what values of \( x \) and \( y \) is the point \((x, y)\) situated in Quadrant III?
  4. For what values of \( x \) and \( y \) is the point \((x, y)\) situated in Quadrant IV?
  5. For what values of \( x \) and \( y \) is the point \((x, y)\) on the \( x \)-axis?
  6. For what values of \( x \) and \( y \) is the point \((x, y)\) on the \( y \)-axis?
Question Part 2: Situational Practice

For each situation, give the coordinates of the point and use the applet to check your answer. (Note: These questions have an infinite number of possible answers).

  1. Point \((x, y)\) is situated in Quadrant II.
  2. Point \((x, y)\) is situated in Quadrant IV.
  3. Point \((x, y)\) is on the \( x \)-axis.
  4. Point \((x, y)\) is situated in Quadrant III.
  5. Point \((x, y)\) is situated in Quadrant I.
  6. Point \((x, y)\) is on the \( y \)-axis.
Answers to Questions in Part 1
  1. A point \((x, y)\) such that \( x \gt 0 \) and \( y \gt 0 \) is situated in Quadrant I.
  2. A point \((x, y)\) such that \( x \lt 0 \) and \( y \gt 0 \) is situated in Quadrant II.
  3. A point \((x, y)\) such that \( x \lt 0 \) and \( y \lt 0 \) is situated in Quadrant III.
  4. A point \((x, y)\) such that \( x \gt 0 \) and \( y \lt 0 \) is situated in Quadrant IV.
  5. A point \((x, y)\) such that \( y = 0 \) is situated on the \( x \)-axis.
  6. A point \((x, y)\) such that \( x = 0 \) is situated on the \( y \)-axis.

More References and Links

Explore additional calculators and graphing tutorials:

Graphing Functions | Graphing Calculators | Home Page