For each exercise:
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.Predict
- What hapens to the mediancentre as you do this?
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.
Predict
- 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.
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