Homework1
A reminder: you are free to collaborate, but you must understand and write up the final answers by yourself!
Write up your answers on a separte sheet. You do not need to include a cover page, but your name and mailbox must be on the first page. Staple multiple pages.

Show that the following sequences commute:
 A rotation and a uniform scaling
 Two rotations about the same axis
 Two translations
Rubric
General proof for any inputs No general cases : 0 Any inputs : 1 Show single commute permutation No transformations : 0 Single way commutes : 2 Show commute permutations are equal Single commutativity : 0 Show both commutes : 2 
Show that any sequence of rotations and translations can be replaced by a single rotation about the origin followed by a translation.
Rubric
Prove basic finite R T cases No transform cases : 0 Proves basic cases : 4 Prove basic infinite R T cases No transform cases : 0 Proves infinite cases : 4 Prove complex infinite R T cases No infinite cases : 0 Proves infinite cases : 5 General proof for any inputs No general cases : 0 Any inputs : 2 
Three vertices determine a triangle if they do not lie in the same line. Devise a test for collinearity of three vertices.
Rubric
Collinear test method No method : 0 Algorithm without justification : 3 Algorithm by example : 6 Justified algorithm : 8 Correct algorithm Does not work at all : 0 Correct for many inputs : 2 Correct for all inputs : 5 General proof for any inputs No general cases : 0 Any inputs : 2