In the previous post, I captured movies of my investigation with The Geometer's Sketchpad. Web Sketchpad allows for including an HTML 5 version of the sketch on a webpage, like this one.
Drag the yellow dot, currently on the triangle to trace out the various positions and area of the triangle.
Note that I have enforced the maximum side length of 10 in a very strange way. Can you describe what I have done? Can you do it in a similar or better way?
Where do you have to place the yellow dot in order to have an area of 0?
How can you drag the yellow dot to keep the area the same?
What other patterns do you see in the behaviour? (There are lots more in the previous post)