Finding transformation T such that T(D*)=D

[toforfiltum]

Homework Statement

If $D^*$ is the parallelogram whose vertices are $(0,0)$,$(-1,3)$, $(1,2)$, and $(0,5)$ and D is the parallelogram whose vertices are $(0,0)$, $(3,2)$,$(1,-1)$ and $(4,1)$, find a transformation $T$ such that $T(D^*)=D$.

Homework Equations

The Attempt at a Solution

From drawing both parallelograms, the point $(0,0)$ maps to $(0,0)$, point $(-1,3)$ maps to $(3,2)$, point $(0,5)$ maps to $(4,1)$ and point $(1,2)$ maps to $(1,-1)$.

I really have no idea how to figure out the transformation. I don't see any pattern at all. Any hints?

Thanks!

 

[Ray Vickson]

Homework Statement

If $D^*$ is the parallelogram whose vertices are $(0,0)$,$(-1,3)$, $(1,2)$, and $(0,5)$ and D is the parallelogram whose vertices are $(0,0)$, $(3,2)$,$(1,-1)$ and $(4,1)$, find a transformation $T$ such that $T(D^*)=D$.

Homework Equations

The Attempt at a Solution

From drawing both parallelograms, the point $(0,0)$ maps to $(0,0)$, point $(-1,3)$ maps to $(3,2)$, point $(0,5)$ maps to $(4,1)$ and point $(1,2)$ maps to $(1,-1)$.

I really have no idea how to figure out the transformation. I don't see any pattern at all. Any hints?

Thanks!

Represent $T$ by a $2 \times 2$ matrix, and figure out what must be the four entries of the matrix.

 

[toforfiltum]

Represent $T$ by a $2 \times 2$ matrix, and figure out what must be the four entries of the matrix.

Ah, thanks. I've got it!