Question

describe a composition of transformations that maps abcd onto abcd.

reflection: about y = x line

reflection: in x - axis

reflection: in y - axis

rotation: 270 degrees

rotation: 180 degrees

reflection: about y = - x line

rotation: 90 degrees

translation

Explanation:

Step1: Analyze the transformation

First, observe the orientation and position of the figure. A rotation of \(90^{\circ}\) (counter - clockwise or clockwise, depending on the coordinate system orientation in the grid) changes the orientation of the figure. Then, a translation (a slide) moves the rotated figure to the final position.

Step2: Check other transformations

• Reflection about \(y = x\) (swaps \(x\) and \(y\) coordinates) would not give the correct orientation and position as in \(A''B''C''D''\).
• Reflection in \(x\) - axis (changes \(y\) to \(-y\)) and \(y\) - axis (changes \(x\) to \(-x\)) do not match the transformation.
• Rotations of \(180^{\circ}\) and \(270^{\circ}\) and reflections about \(y=-x\) (swaps \(x\) and \(y\) and changes their signs) do not result in the correct mapping.

Answer:

Rotation: 90 degrees, Translation