We began the morning with an investigation of features of the version 3.0 of the Geometer's Sketchpad.

1. Annie gave us the following exercise:

    - Open a new Sketchpad window and create x and y axes.  

    - Create three points, A, B, and X on the x axis, and 
      find their coordinates.

    - Using the calculator, calculate the x coordinate of each 
      (hereafter these coordinates will be called simply 
      X, A, and B).
                                        2
    - The equation to plot is  F(X) = AX  +  B  
                                        2
    - Using the calculator, calculate AX + B

    - Select X and this equation and, using the calculator, 
      plot x,y (graph menu).

    - Move X along the x axis until the point x,y appears 
      on the screen.

    - Find the locus of x,y as X moves along the x axis:

    - Select X, the x axis, and x,y and construct
      the locus (Construct menu).

    - Move A and B and describe the results.

PARABOLA!

2. Next we looked at a geometric representation:

   - draw line segment AB

   - put a point C somewhere not on it (slightly above)

   - construct a point X on the line and connect C and X

   - select line CX and construct its perpendicular bisector

   - select line CX and trace locus

   - make an Animate button

   - Question: How do you find the point on the perpendicular 
               bisector of CX that is on the parabola?

PARABOLA!