The Friday Fave would like to tel youl about a very handy calculator feature, and then invite you to do some math.
The feature first.
Imagine you’ve got a set of points, and you’ve named them A, B, C,
and D. You probably want to make a quadrilateral from those four points, and
it used to be difficult but now it is easy.
What sort of thing is a quadrilateral? Why, it’s a polygon. So you just tell the Desmos calculator that you want to make a polygon with those four points, and boom!
Alternatively, you may have specified the x-coordinates of your quadrilateral with a list, and the y-coordinates with another. Do not ask the Fave how the calculator can interpret two lists just as easily as it can interpret four points, but it can.
This second version of polygon is especially handy because you can operate on a list (you cannot yet operate on points except by dragging them around). So now let’s do a little math together, shall we?
What do you suppose our polygon will look like if we type polygon(X,Y-4)? Click through on the expression to find out.
What about polygon(2X,Y)?
And finally, what will polygon(Y,X) look like?
Bonus question: What transformation do you need to apply to make our polygon no longer be a kite, and how might we express that transformation algebraically?
Now that the Fave has you thinking about polygons, here are some delightful ways to extend your thinking…