Author: G. T. Springer (original article)
In this short article, we discuss how to use the HP Prime Advanced Graphing app to teach students about transformations in the plane, including translations and reflections.
But instead of a geometric approach, the app allows us to take an algebraic approach. We start with a generic shape, which we then transform in various ways to build a picture of a rose.
We start by defining our generic shape, a filled ellipse, given by
V1and choose purple
A reflection over the vertical line x=−1 is a mapping such that x→−2−x and y→y.
So we define
V2 to be
V1(-2-X,Y), as shown in the figure. We use the same color (purple) for our reflection.
We need a stem for our rose. Creating a stem takes some experimentation. Students will learn to stretch the base shape first, then translate it into its final position.
V3 to be
V1(10*(X+1),0.3*(Y+4)), as shown to the right.
Do not forget to change the color to dark green!
Next, we add some leaves.
For the first leaf (in
V4), we experiment as we did for the stem, first dilating and then translating to get what we want.
Then the second leaf is the reflection of the first leaf, using the same method we used for the petals.
We chose light green as the color for both leaves.
And now you have a simple rose!
For extra credit, we added two fancy petals and some thorns. The expressions are shown on the next page in case you want to work them out for yourself first!
Be sure to save your new app. Press
ARose4You), and tap
If you are using the HP Virtual Prime for the PC (it is on the product CD that came with your HP Prime), you can just copy and paste the expressions below into the virtual calculator. Then you can send the app from the virtual calculator to your physical HP Prime. The steps are listed below.
Advanced Graphing app expressions for the rose:
Y+1>(X+1)^2 AND Y<1+COS(2*X+3)