Question

1. quadrilateral abcd was rotated 90 degrees counterclockwise about the origin and then reflected over the y-axis. identify which side lengths are equal.

ad =
dc =
cb =
ab =

Explanation:

Step1: Recall Transformations' Effect

Rotations and reflections are rigid transformations. Rigid transformations (translation, rotation, reflection) preserve side lengths and angle measures of a figure. So, after rotating 90° counterclockwise about the origin and reflecting over the y - axis, the image of quadrilateral \(ABCD\) (let's call it \(A'B'C'D'\) or the figure \(P\) with sides \(p, m, n, o\)) will have side lengths equal to the corresponding sides of \(ABCD\).

Step2: Match Corresponding Sides

• For side \(AD\): After the rigid transformations, the side corresponding to \(AD\) in the transformed figure (Figure \(P\)) should have the same length. Looking at the labels, the side equal in length to \(AD\) is \(p\) (since rigid transformations preserve side lengths, \(AD = p\)).
• For side \(DC\): The side corresponding to \(DC\) in the transformed figure is \(m\) (because rigid transformations keep side lengths, so \(DC=m\)).
• For side \(CB\): The side corresponding to \(CB\) in the transformed figure is \(n\) (as rigid transformations preserve side length, \(CB = n\)).
• For side \(AB\): The side corresponding to \(AB\) in the transformed figure is \(o\) (since rigid transformations preserve side length, \(AB=o\)).

Answer:

\(AD = p\), \(DC = m\), \(CB = n\), \(AB = o\)