Question

describe a composition of transformations that maps abcd onto abcd
rotation: 180 degrees
rotation: 270 degrees
reflection: about y=x line
reflection: in x - axis
reflection: in y - axis
reflection: about y=-x line
translation
rotation: 90 degrees

Explanation:

Step1: Analyze rotation of 180 degrees

A rotation of 180 degrees about the origin changes the coordinates \((x,y)\) to \((-x,-y)\). Let's assume a point \(A(x,y)\) in \(ABCD\). After a 180 - degree rotation about the origin, it will be mapped to \(A'(-x,-y)\) which is consistent with the transformation from \(ABCD\) to \(A'B'C'D'\) in the grid.

Step2: Analyze other transformations

• Rotation of 270 degrees: A 270 - degree rotation about the origin changes \((x,y)\) to \((y, - x)\), which does not match the transformation in the grid.
• Reflection about \(y = x\): Changes \((x,y)\) to \((y,x)\), not matching.
• Reflection in \(x\) - axis: Changes \((x,y)\) to \((x,-y)\), not matching.
• Reflection in \(y\) - axis: Changes \((x,y)\) to \((-x,y)\), not matching.
• Reflection about \(y=-x\): Changes \((x,y)\) to \((-y,-x)\), not matching.
• Translation: A translation would slide the figure without rotating, which is not the case here.
• Rotation of 90 degrees: A 90 - degree rotation about the origin changes \((x,y)\) to \((-y,x)\), not matching.

Answer:

Rotation: 180 degrees