Transforming the Square - Introduction
We are assuming that students working through this module will have basic experience with Desmos and the use of parametric equations. We have introduced these ideas in our Parametric Thinking Activity, so if you haven't done that one yet you can start there and then come back!
For this activity we start by looking at a 2×2 square centered at the origin and a 1×4 rectangle centered at the point (8,6). Our objective is to transform the square to the rectangle continuously over a time period of {0 ≤ T ≤ 1}. We want the colours to match as well—every line from the original square has to land on its corresponding line in the rectangle.
There are lots of ways to do this, for example with a continuous dilation and rotation.
Hang on! That can’t work. The square and the rectangle have different orientations––one cannot be rotated onto the other, even with a change in shape.
Well, actually there is a way––use a negative number in your dilation. There’s something there to play with.