Question

Figure ABCD is transformed to obtain figure A′B′C′D′:

DIAGRAM INCLUDED! 100 Points!

Part A: Write the sequence of transformations that changes figure ABCD to figure A′B′C′D′. Explain your answer and write the coordinates of the figure obtained after each transformation. (6 points)

Part B: Are the two figures congruent? Explain your answer. (4 points)

Answer 1

Part A

1. Reflect over the y-axis: (x, y) → (-x, y)
   A (-4, 4) → (4, 4)
   B (-2, 2) → (2, 2)
   C (-2, -1) → (2, -1)
   D (-4, 1) → (4, 1)
   
2. Shift 4 units down: (x, y-4)
   (4, 4-4) → A' (4, 0)
   (2, 2-4) → B' (2, -2)
   (2, -1-4) → C' (2, -5)
   (4, 1-4) → D' (4, -3)

Part B

Two figures are congruent if they have the same shape and size. (They are allowed to be rotated, reflected and translated, but not resized).

Therefore, ABCD and A'B'C'D' are congruent. They are the same shape and size as they have only be reflected and translated.