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Transformations

Using the graphing calculator to examine transformations:

Figure being used will be a triangle:   A(1,1), B(6,3), C(4,7).
1.   Clear entries in the Y= positions (or turn them off).

2.   Turn on the Connected Graph icon under StatPlots.
Go to StatPlot - #1 Plot - highlight On - highlight second icon. 
Xlist is the name of the list where the x-coordinates will be found.
Ylist is the name of the list where the y-coordinates will be found.
Mark:  choose the heavier mark to represent the original figure.
pic1

3.  Enter values into L1 and L2.  Enter the x-coordinate in L1 and its corresponding y-coordinate in L2.  Enter the first coordinate again at the end to complete the connected drawing.
(See Basic Commands for help entering data in lists.)

The original triangle is now residing in Plot1.  When graphing do NOT choose ZoomStat for the window.  We want to have a coordinate axes for examining our transformations.  Use a standard 10x10 window (ZStandard) for this problem.

4.   We will be placing our transformation coordinates into L3 and our transformation figure will reside in Plot2.
pic2

transpic1

  
Reflection over the x-axis: (negate y-values)

Store the negated y-values into list L3.  You can type them in yourself or let the calculator create the values.  Arrow up ONTO L3 and enter - L2 (to negate the y-values).  Press ENTER.

trans4

Set up Plot2:  Xlist:  L1 and Ylist:  L3
(I like to choose a different "Mark" so that the transformation can be easily distinguished from the original drawing.)

transf2      transf3

 
Reflection over the y-axis: (negate x-values)

Let L3 be -L1.  Under Plot 2, assign Xlist: L3 and Ylist:  L2.  Graph.

tf4   tf5   tf6


Reflection over the line y = x: (switch coordinates)

Under Plot 2, assign Xlist:  L2 and Ylist:  Y1.  Graph.  Your might also wish to graph Y1= x to show the line of reflection.

 tf7   tf8   tf8


Reflection in origin: (negate both coordinates)

Let L3 = -L1.  Let L4 = -L2.  Under Plot 2, assign Xlist:  L3 and Ylist:  Y4.  Graph. 

 tf10   tf11   tf12


Translation (x,y) → (x - 7, y - 2):

Let L3 = L1 - 7.  Let L4 = L2 - 2.  Under Plot 2, assign Xlist:  L3 and Ylist:  Y4.  Graph.

 tf13   tf14   tf15


Dilation of scalar factor 2: (in the origin)

Let L3 = L1 * 2.  Let L4 = L2 * 2.  Under Plot 2, assign Xlist:  L3 and Ylist:  Y4.  Graph.  Adjust the window to see the dilation.

 tf16   tf17   tf18
tf19
       

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