Question

question 1-8
rectangle defg has vertices d, e, f, and g. under which transformations are both ef = ef and ∠def ≅ ∠def? select all that apply.
□ rotation 270° counterclockwise about point d
□ dilation about the origin with a scale factor of 2.
□ translation along the vector < -5,7 >
□ reflection in the x - axis
□ all of the above

Explanation:

Step1: Recall properties of transformations

Rigid - motions (rotations, translations, reflections) preserve side - lengths and angle - measures. Dilations change side - lengths.

Step2: Analyze rotation

A rotation of 270° counter - clockwise about Point D is a rigid motion. It preserves side - lengths and angle - measures. So, EF = E'F' and ∠DEF≅∠D'E'F'.

Step3: Analyze dilation

A dilation about the origin with a scale factor of 2 changes the side - lengths. If the scale factor is 2, EF≠E'F'.

Step4: Analyze translation

A translation along the vector < - 5,7> is a rigid motion. It preserves side - lengths and angle - measures. So, EF = E'F' and ∠DEF≅∠D'E'F'.

Step5: Analyze reflection

A reflection in the x - axis is a rigid motion. It preserves side - lengths and angle - measures. So, EF = E'F' and ∠DEF≅∠D'E'F'.

Step6: Analyze 'All of the above'

Since dilation does not preserve side - lengths, 'All of the above' is incorrect.

Answer:

A. Rotation 270° counterclockwise about Point D
C. Translation along the vector < - 5,7>
D. Reflection in the x - axis