The components of the ordered pairs can be either the Cartesian coordinates(x,y) or the polar coordinates(r,θ).
To plot, for example, the points (1,2), (3,4) simply enter them as follows (spaces are optional): 1,2; 3,4;
For plotting points with polar coordinates, simply select the polar coordinate system using the Polar checkbox provided, and type in the coordinates. The angle θ can be entered in radians, degrees, or grades.
You can also connect the points with line segments to form line graphs and polygons.
Rotate Axes and Plot Points
This unique points plotter enables you to rotate any of the coordinate axes to create point and line graphs in oblique coordinate systems (non-orthogonal Cartesian and generalized polar coordinate systems), where the axes can be rotated to any angle and have any orientation.
Note: Our graphing software allows you to use constant expressions, such as π or 1+√(2) wherever you can use a literal number.
Instructions for Points Grapher (Cartesian and Polar)
Our advanced points grapher is easy to use; simply enter the coordinates of a set of points with the following syntax. The points are plotted as you type (default).
Entering Points
The points (a1,b1),(a2,b2),... are entered as
a1,b1; a2,b2; ...
In other words, separate the coordinates of each point by a comma and the points themselves by a semicolon (note that parentheses are excluded). The last semicolon is optional, see the note below.
You can use constant expressions such as 1/2+sin(π/3) for point coordinates.
Example: 1,2; 3/4,4; -2,sin(π/6); (This will plot three points). If you choose the DEGREE mode, you can simply type in sin(30) since π/6 (RADIANS) is equal to 30°.
Points grapher: Points graph in Cartesian coordinate system, and line graph (polygon) formed by connecting the points.
Points grapher: Points and polylines (polygon) in oblique Cartesian coordinate system.
Polar points grapher: Points and line graphs in polar coordinate system.
Polar points grapher: Points and line graphs in oblique polar coordinate system.
Plotting Point Sets in the Polar Coordinate System
To draw the points in the polarcoordinate system as (rn,θn), select the Polar checkbox. The coordinate grapher enables you to input angular coordinates (radial angles) in various units–radians, degrees, and grades by selecting the corresponding angle mode..
Connecting Points
To connect the points in the focused expression box with line segments, press the Connect toggle button. You can press it again to disconnect the points.
Note: When connecting the points, if the last point is followed by a semicolon, it will be connected to the first point to form a (closed) polygon.
Graphing Multiple Sets of Points
To graph multiple point sets, press the » button to show the multi-graph pane with expression panels.
Add or delete panels with the + or × buttons if necessary.
Select or deselect checkboxes to show or hide graphs.
Labeling Axes
To label an axis, click on the ▼ icon at the top right of the canvas. Type in any number for which you want to label the axes, and press the Label button. You can also use constants like π, or even constant expressions such as 1+3π/2.
Rotating Axes
Our graphing software offers a unique feature: axis rotation. This allows you to visualize the graph of a given set of points in the oblique (non-perpendicular) coordinate system. To rotate an axis, click on the ▼ icon at the top right of the canvas, and then enter the angles by which you want to rotate an axis and press the Rotate button. The axis will rotate and the graphs will be redrawn to reflect the rotation.
Copying & Saving Graphs
Click the Copy/Save graph button. This will create a copy of all the graphs on the canvas (graphing area) which will appear as an image below the graphing calculator..
Right-click on the image and select the appropriate option from the context menu. Depending on your device and preferences, you might be able to:
Copy: Create a copy of the image to your clipboard for pasting elsewhere.
Save image as... : Save the image as a file on your device in a chosen format (e.g., PNG, JPG).
Mouse Operations in Our Graphing Software
Our graphing software allows you to use your mouse to perform unique operations as outlined below.
How to Rotate Axes
You can also use your mouse to rotate an axis: Hold down the Alt key and click on or near the axis. This will select the axis, and its color will change to red. Move the mouse. The selected axis will rotate accordingly, and the graphs are redrawn to reflect the rotation of the axis. Click again with the Alt key pressed, to release the axis.
To restore the coordinate system to its normal state press the Reset button (if hidden, press the ▼ icon).
How to Change Scales
To change the scale (zoom in one direction), hold down the ctrl key and click on an axis. The point that was clicked will be labeled "1" if clicked on the positive side, or "-1" if clicked on the negative side of the axis; it becomes the new unit for that axis.
How to Translate the Coordinate system
You can move the coordinate system in one of the following ways:
Click on the canvas and drag the mouse; this will translate the origin and the graphs together.
Double-click on the canvas to move the origin to the location where you clicked; the graphs are updated.
Settings
Press the ⚙ (gear) button to set options (if the button is hidden, first click on the ▼ icon at the top right of the canvas):
Change graphthickness using the slider.
Select the angle mode (radians - default, degrees, grades).
If you deselect the Graph as you type option, you will have to press Graph selected expressions, which then appears at the bottom of the calculator, to update the graphs whenever you make any changes to the expressions or the coordinate plane (i.e., move the origin, rotate axes, etc.).
You have the option to display controls that will automatically rotate the axes.
The points plotter remembers the expressions so that you can use them in future visits. You can press Reset Calculator to clear them.
Points in Oblique Cartesian Coordinate System
One of the most interesting features of our point grapher is the ability to rotate the axes. The standard Cartesian coordinate system, typically referred to as the rectangular coordinate system, employs two perpendicular axes. By rotating these axes, we create a Cartesian coordinate system where the axes intersect at any angle. This is known as an oblique Cartesian coordinate system, distinct from its rectangular counterpart.
Our graphing tool uniquely allows exploration of how points appear in this generalized Cartesian coordinate system, which we term the oblique Cartesian coordinate system or simply the oblique coordinate system.
While many texts use "Cartesian" and "rectangular" coordinate systems interchangeably, both typically refer to the rectangular Cartesian coordinate system with perpendicular axes. To differentiate it from the oblique Cartesian coordinate system we introduce, we use the full term rectangular Cartesian coordinate system.
Given the novelty of this feature in our software and the lack of specific online resources for oblique coordinate systems, we categorize an oblique coordinate system as a specialized type of Cartesian coordinate system. To distinguish it from the rectangular Cartesian coordinate system, we have coined the term oblique Cartesian coordinate system.
By accommodating oblique axes, our grapher offers fresh perspectives for data visualization and analysis, particularly in fields like physics, engineering, and geometry where non-orthogonal coordinate systems can streamline complex problems.
Points in Oblique Polar Coordinate System
In the standard polar coordinate system, the polar axis is drawn horizontally. However, our polar points plotter allows you to position it at any angle and orientation by rotating the axis. This enables you to plot any set of points in an oblique polar coordinate system.
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