### Geometry Forum Summer Institute - July 9-15, 1995

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### Sketchpad Investigations Thursday, July 13, 1995

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,

- 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

- 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?
```