which composition of transformations maps figure efgh to figure efgh?\n a reflection across line k followed…

which composition of transformations maps figure efgh to figure efgh?\n a reflection across line k followed by a translation down\n a translation down followed by a reflection across line k\n a 180° rotation about point g followed by a translation to the right\n a translation to the right followed by a 180° rotation about point g

which composition of transformations maps figure efgh to figure efgh?\n a reflection across line k followed by a translation down\n a translation down followed by a reflection across line k\n a 180° rotation about point g followed by a translation to the right\n a translation to the right followed by a 180° rotation about point g

Answer

Explanation:

Step 1: Analyze transformation effects

Reflections reverse orientation; translations shift position. Rotations around a point change orientation and position based on center.

Step 2: Evaluate order importance

Transform order matters: reflecting then translating vs. translating then reflecting yields different results. Rotating around point G keeps G fixed during rotation.

Step 3: Assess options

  • A: Reflection over line k (flips over k) then translation down (shifts down) could map EFGH to E'F'G'H'' if orientation and position match.
  • B: Translation down first would move figure before reflection, likely misaligning with k.
  • C: 180° rotation around G (fixes G) then translation right: G would move right after rotation, but rotation center G should stay fixed post-rotation (contradiction).
  • D: Translation right first moves G, then rotation around original G would misplace G''.

Answer:

A. a reflection across line k followed by a translation down