Navigate to http://www.math.union.edu/locate/MFA-09-2008/evolver.html to complete this assignment.

For each exercise:

1. Try to predict what will happen, before using the software. First write down your own prediction, then describe it to the rest of the group.
2. Test your predictions by playing with the program. Discuss the results, and write down a revised group answer, based on what you learned.
3. Finally, explain the revised predictions.

These questions are for the mediancentre only.

A. Case 1: Start with three points forming a triangle, and add a fourth point not inside the triangle formed by your first three points.
• What happens to the mediancenre as you shift around the four points, begin careful never to let any point lie inside the triangle formed by the other 3?
• Try to find a general rule for predicting the position of the mediancentre of four points that meet the condition in italics above.

Predict

Test & Revise

Explain

B. Transition: Begin to move one of the points along a straight line directly towards the mediancentre until it reaches the mediancentre.
• What hapens to the mediancentre as you do this?
Predict

Test & Revise

Explain

C. Case 2: When your moving point reaches the mediancentre, continue to move it in the same direction, staying on the same straight line path. Keep moving the point in the same direction until you feel confident that nothing really new will happen.

• What happens to the mediancentre as you do this?
• Create a general rule for predicting the mediancentre of four points when one of the four is inside the triangle formed by the other three.
Predict

Test & Revise

Explain

D. General Case: Try to find a general rule (expressed using cases, as we did for triangles) for predicting the location of the mediancenre of any four points. (Hint: do the 2 cases above cover all the situations?)

Predict

Test & Revise

Explain