1 left and 2 down - 

$$\begin{pmatrix} -1 \\ -2 \\ \end{pmatrix}$$

1 right and 2 up - 

$$\begin{pmatrix} 1 \\ 2 \\ \end{pmatrix}$$

2 right and 1 up - 

$$\begin{pmatrix} 2 \\ 1 \\ \end{pmatrix}$$

2 right and 1 down - 

$$\begin{pmatrix} 2 \\ -1 \\ \end{pmatrix}$$

2 left and 1 up - 

$$\begin{pmatrix} -2\\ 1 \\ \end{pmatrix}$$

1 right and 2 up - 

$$\begin{pmatrix} 1 \\ 2 \\ \end{pmatrix}$$

P'(-2, -3) - 

$$x= 0$$

P'(2, 3) - 

$$y = 0$$

P'(-3, 2) - 

$$y=-x$$

P'(3, -2) - 

$$y=x$$

Button a - 

translates object

Button b - 

rotates object

Button c - 

enlarges (dilates) object

Button d - 

creates a polygon

Shape A to shape B - 

Rotation $$90$$° clockwise about $$(4, 1)$$

Shape B to shape C - 

Translation by $$\begin{pmatrix} -4 \\ -5 \\ \end{pmatrix}$$

Shape C to shape D - 

Reflection in the line $$x=4$$

Shape D to shape E - 

Enlargement, scale factor $$2$$, about $$(6,-3)$$