Rotating a triangle
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
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?