This section explains how to use points (labels) and vectors in the Desmos Graphing Calculator.

Points

You can draw a point by writing something like $(1,2)$. You can change the appearance of the point from the settings on the left of the expression.

Labels

By checking the label option, you can add a label to a point.

If you hide the point while keeping the label checked, you can display only the label. This is useful for adding text to the graph.

Displaying Variable Values

In a label, writing ${variableName} will display the value of that variable.

For example, if $a=11$, setting the label to a=${a} will display a=11 on the graph.

If you change the value of $a$, the value displayed on the graph will also update accordingly.

Note

You can change the label display settings from the options on the left.When embedding variables in labels, as shown in the graph above, click the right arrow to align the label to the left. Otherwise, the label will shift based on the length of the variable.

Displaying Equations with TeX

Enclosing a label with ` (backticks) will render its content as $\TeX$.

Note that it is ` (backticks), not ' (single quotes).

$\TeX$ is a widely used typesetting system for displaying equations beautifully. Refer to other resources for more details.

If you enclose the equation part of the label in backticks, it will look like the graph below.

Draggable Mode

By using variables for the coordinates of a point, such as $(a,b)$, you can create draggable points.

You can change how the point can be dragged from the settings on the left.

Additionally, for example, $(a, a^2)$ will allow the point to be dragged along a parabola, and setting a range for the variable will restrict the draggable area.

The major advantage of this feature is that you can visually manipulate the values of variables tied to the coordinates of the point.

For example, as shown below, you can visually move the entire graph by dragging the point.

Vectors

Points can also be treated as vectors. In addition to basic operations, they are useful in parametric representations.

Additionally, you can reference the $x$ or $y$ coordinate of a vector using $(1,2).x$ or $(1,2).y$.

Using this, you can create functions to rotate vectors by a specific angle, for example.

The 2D version does not have a function to directly draw vectors. Using polygon(), as shown in the graph above, is a good alternative.