Move any of the vertices and notice what happens to Area and P(erimeter).[br][br]Return to a triangle about the same size (or press the undo button or refresh this page) with an Area of 2.[br][br]Move a purple point to one of the vertices. Now click on middle of the triangle (to select it) and move the same vertex to a point where the triangle's Area is 2. Drag a point to this new location. [br][br]Repeat for at least 8 purple points: Click the triangle again and move the same vertex to another location where the area is 2. Drag another purple point to this location.[br][br]What do you notice? How could you use the tools to confirm any patterns you might see? How might this relate to the formula for the area of a triangle?

Refresh this screen to reset the figure.[br][br]If you want, you can move or change the triangle. The triangle you end up with should have a P(erimeter) of 6.5.[br][br]As with the area earlier, move a purple point to one of the vertices of your triangle. [br][br]Click the triangle and move this same vertex to a point where the P(erimeter) is 6.5. Drag another purple point to the new location of the vertex. [br][br]Repeat clicking the vertex, moving it to a new location (P=6.5) and moving a purple point to this location.[br][br]What pattern seems to be emerging from the collection of points? [br][br]For which of the points was the Area near, or at, a maximum value? [br][br]How might your results be related to the orbit of Halley's comet?[br]https://en.wikipedia.org/wiki/Halley%27s_Comet#/media/File:Halley's_Comet_animation.gif[br][br][br]