Question

the figure shows a game in which the object is to create solid rows using pieces given. using only translations and rotations, describe the transformations for each piece at the top that will form two solid rows at the bottom.

Answer 1

There are other possible solutions to this problem. For example, we could rotate the blue piece by 270 degrees counterclockwise instead of 90 degrees counterclockwise. This would also move the blue piece to the right side of the grid, forming a solid row with the yellow piece.

To create two solid rows using the pieces given in the image using only translations and rotations, we can use the following transformations:

Purple piece:

• Rotation by 180 degrees counterclockwise about the origin.
• Translation by (x - 5, y - 6).
• This will move the purple piece to the bottom right corner of the grid, forming a solid row with the green piece.

Green piece:

• Translation by (x, y + 1).
• This will move the green piece up one row, forming a solid row with the purple piece.

Blue piece:

• Rotation by 90 degrees counterclockwise about the origin.
• Translation by (x + 1, y).
• This will move the blue piece to the right side of the grid, forming a solid row with the yellow piece.

Yellow piece:

• Translation by (x - 1, y).
• This will move the yellow piece to the left side of the grid, forming a solid row with the blue piece.