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…

Polygraph: Advanced Quadrilaterals