Final answer:
To show that triangle J is congruent to triangle P, a valid transformation sequence is a reflection across a vertical line followed by a 90° clockwise rotation as suggested in option (d), assuming that the positions of the triangles require this sequence for congruence.
Step-by-step explanation:
The student's question about which sequence of transformations can be used to show that triangle J is congruent to triangle P involves understanding the properties of geometric transformations. Congruent triangles mean that they have the same shape and size, but their positions may differ. To demonstrate that two triangles are congruent, one might perform a series of transformations such as reflections, rotations, and translations that map one triangle onto the other without altering its size or shape.
For the given options, a reflection followed by a rotation is suggested to map triangle J onto triangle P. It is important to know that a reflection across a line followed by a 180° rotation would essentially result in the triangle being in the same orientation as before because two such successive movements cancel each other out in terms of orientation. However, a reflection followed by a 90° rotation would change the triangle's orientation relative to its original position.
Option (d), which is a reflection across a vertical line followed by a 90° clockwise rotation, is a valid sequence that could be used to demonstrate congruence if triangle J and triangle P are in such positions that this sequence of transformations maps one onto the other exactly.