Rotating a triangle

PROBLEM:

Find the locus of the third vertex of an triangle when two of its vertices are moved along the x-axis and y-axis respectively.

1. Try cutting a triangle out of cardboard and doing some exploration "by hand."

2. Implement this with GSP and trace the locus of a triangle "rotating" as described. The implimentation requires finding a way to move the two vertices along the axes and keep the sides of the triangle fixed.

The rotation produces the following locus:

Click here for the GSP sketch. The lengths of the sides of the triangle can be adjusted to explore other shapes.

3. Determine equations and implement the equations in a graphing program. This is readily accomplished using parametric equations. See Problem 8 in EMT 668 Assignment 10 for a discussion of such parametric equations.

4. What happens if the triangle being rotated is a right triangle with the hypotenuse connected to the x and y axes?