Parametric Triangle 1

https://www.desmos.com/calculator/mb3pfwffxm

We begin by asking the students to construct:

·       an initial triangle             

·       a final triangle                   

as shown in the diagram. We have them plot and label the vertex points and then use the polygon function to draw the triangles.

We ask them to construct a red triangle, , whose vertices move, in time 0≤T≤1 in a straight line at constant speed between the corresponding vertices of the initial and the final triangles. The diagram at the right depicts the red triangle at T = 0.5 such that vertex A is ½ of the way along in its journey from  to .

(a) Is the red triangle ever simply a line? And if so, at what time?

(b) Is the red triangle ever isosceles? The answer is yes—at T = 0 and at T = 1. But are there other times?