Using the capabilities of the Computer Algebra System (CAS) behind Grasple it is possible to create exercises that allow your students to practice with points / coordinates. Below we explain all ins-and-outs of the support of this constructs within the platform.

# Syntax

Points in a 2-dimensional space are defined by enclosing two numbers (or expressions) between parenthesis. Thus, `(0, 0)`

represents the origin of a two-dimensional space, just as `(1-1, 0)`

and `(0, -2 + 2)`

.

The platform supports N-dimensional points using the same notation, e.g. `(0, 0, 0)`

for three dimensions, `(0, 0, 0, 0)`

for four dimensions, etc.

# Equality

Two points are equal if all individual elements are equal. As usual, the algebraic equality will evaluate whether two expressions are the same. This means that the following expressions are considered to be equal:

If you do not want to allow the CAS to evaluate the expressions while checking the answers you can use the *exact* check. More information about this check can be found in this article.

# Operations

In the current implementation it is not possible to add or subtract points. It is possible to use some of the available operators on points specified by either you or your students. In particular, the `select`

and `length`

operators work on points in the same way they work on lists.

# Points versus Intervals

By default the expression `(1, 3)`

is interpreted as a point. If you want to make sure the answer of a student is interpreted as an open interval you can follow the instructions in this article.