If you are going to rotate any of the pieces, rotate it about one of its vertices and not about the origin.
Piece
Translation
Rotation
Red
(x,y)→ (x+3,y-7)
-
Orange
(x,y)→ (x+4,y-6)
90^(∘)
Purple
(x,y)→ (x-2,y-6)
180^(∘)
Practice makes perfect
The only way to create two solid rows using the given pieces is by placing them like below
Let's assume we cannot translate or rotate a piece if that action collides it with another piece. Since the red piece only requires translations we will start with this piece. To place it in its right spot, we first translate it 4 units down, followed by 3 units to the right and then another 3 units down.
These translations can be expressed as
(x,y)→ (x+3,y-7).
Let's turn to the orange piece. In addition to translating the piece down by a total of 6 units and to the right by 4 units, we also need to rotate it 90^(∘) counterclockwise.
These combinations of translations can be expressed as
Translation:& (x,y)→ (x+4,y-6)
Rotation:& 90^(∘)
Finally, we will turn to the purple piece. In addition to translating the piece down by a total of 6 units and to the left by 2 units, we also need to rotate this piece 180^(∘) counterclockwise.
These translations can be expressed as
Translation:& (x,y)→ (x-2,y-6)
Rotation:& 180^(∘)
