Part #1

Compute a 3 by 3 transfomation matrix that composes a translation by t_x, t_y and a rotation by q such that the translation is first and the rotation second. Is the resulting transformation in the Euclidean Group?

Part #2

Compute the affine transformation that maps the vertices of a triangle v₁, v₂, and v₃ to the canonical triangle with vertices (1,0), (0,1) and (0,0) respectively. Show how this transform can be used to map any triangle to any other triangle.

Limit your work to a single sheet of 8.5" by 11" paper.