In response to Nicholas Jackiw in response to my response to Gilles Jobin:
Just to extend Eileen Shoaff's excellent suggestions a bit...
[Gilles Jobin writes:] >> Could we represent the length of a segment with >> a "letter" and use the calculator to make all the necessary >> calculation? ... >> We could then represent thing like 2n^2 + n + 3 "geometrically" but >> still have an unknow to deal with.
[To which Eileen Shoaff replies:] > You can certainly construct a segment and label it "n". > You can then construct a square of side n, area = n^2. > Then you can drag to vary n to see the change in the square and value of n^2. > To obtain 2n^2 + n + 3, you need to decide what 1 is. This is determined by the unit chosed in preferences, or it can be defined. ... > I like to set the preferences at cm. Then I > place a point on the screen, then translate it 1 cm. Now I construct a 1 cm segment, then choose it at the unit for the graph.
Pursuing the premise that within dynamic geometry, the more variables, the better (because variables can be changed dynamically; constants can't), here are a few further ideas:
* When you create a grid, its default unit length is equal in length to the current preferred Distance unit (i. e. 1 cm or 1 inch). The advantage of using the default grid, instead of a coordinate system in which you've fixed the unit at 1 cm for all time, is that the default grid's unit length can be dynamically varied from its default size. This is handy when you graph turns out to be too large to fit on the screen, etc.
* Alternately, if you're convinced you want to fix the size of a unit, note that you can fix it at any concrete distance. You can either construct a segment of fixed length using translation, as Eileen does, or you can just create a constant length by typing it into the calculator (e. g. "3.5 cm"). Then, select the length (expressed either as a segment or a measurement) and choose "Set Unit Length" from the Graph menu.
Okay -- I didn't know this. What I wanted to do was to place points on the screen using coordinates to create an odd shaped area. I then wanted students to determine the area using two methods: Pick's Theorem and by constructing a rectangle around the shape and subtracting off the pieces outside the shape. I then wanted them to be able to check by having GSP give the area. I needed to have the unit of the axes = the unit in the preferences. I did not want the students to drag the B point and change the size of the unit on the axes, otherwise the area wouldn't be correct. I also found it nearly impossible to make a segment exactly 1 cm long, so I devised the translate method.
See what happens when you don't read the manuals! You have to use your wits alone.