Question

triangle def and triangle def are shown. choose two transformations that will map triangle def onto triangle def. a. 180° rotation about the origin b. a 90° clockwise rotation about the origin followed by a translation 8 units down c. a reflection across the y - axis followed by a reflection across the x - axis d. a reflection across the x - axis followed by a 90° clockwise rotation about the origin e. a reflection across the x - axis followed by a 180° counter - clockwise rotation about the origin

Explanation:

Step1: Analyze rotation rules

A 180 - degree rotation about the origin changes the sign of both the x - and y - coordinates of each point. If we rotate triangle DEF 180 degrees about the origin, it will map onto triangle D'E'F'.

Step2: Analyze reflection - translation combinations

A reflection across the y - axis changes the sign of the x - coordinate of each point. Then a reflection across the x - axis changes the sign of the y - coordinate of each point. This combination of reflections is equivalent to a 180 - degree rotation about the origin and will map triangle DEF onto triangle D'E'F'.

Answer:

A. 180° rotation about the origin
D. a reflection across the y - axis followed by a reflection across the x - axis