The correct answer is a) gluteus maximus.
The gluteus maximus is the largest muscle in the buttock region and plays a crucial role in the movement of the hip joint. It is primarily responsible for extending the thigh at the hip joint, which is the action of moving the thigh backward. This muscle also aids in laterally rotating the thigh, helping with movements such as walking, running, and climbing stairs.
Other muscles mentioned, like the gluteus medius and gluteus minimus, are more involved in stabilizing the pelvis and abducting the thigh rather than primarily extending it. The piriformis also assists in lateral rotation but is not primarily a thigh extensor. Finally, the tensor fascia latae is mainly involved in hip flexion and abduction. Therefore, while all these muscles play important roles in hip movement, the gluteus maximus is unique in its primary function of extending and laterally rotating the thigh.