Question

4a is figure efgh an image of figure abcd after a rotation using center p? explain your reasoning with math vocabulary.

Explanation:

Step1: Recall rotation properties

In a rotation, the distance from the center of rotation to each point in the pre - image is equal to the distance from the center of rotation to the corresponding point in the image. Also, the angle of rotation for all corresponding points is the same.

Step2: Check corresponding distances

If we assume that the transformation from figure ABCD to figure EFGH is a rotation about point P, we need to check if \(PA = PE\), \(PB=PF\), \(PC = PG\) and \(PD=PH\). If these equal - distance relationships hold for all corresponding points, and the angle of rotation for each pair of corresponding points about point P is the same, then EFGH is the image of ABCD after a rotation about P.

Step3: Check angle of rotation

We also need to verify that the angle of rotation between any pair of corresponding points (e.g., \(\angle APE\), \(\angle BPF\), \(\angle CPG\), \(\angle DPH\)) is the same. If all these conditions are met, then figure EFGH is an image of figure ABCD after a rotation using center P.

Answer:

We need to check if the distances from point P to corresponding vertices of ABCD and EFGH are equal and if the angles of rotation for all corresponding points about P are the same to determine if EFGH is the rotated image of ABCD about P.