Figure abcd is transformed to obtain figure a'b'c'd':

a coordinate grid is shown from negative 6 to 6 on both axes at increments of 1. figure abcd has a at ordered pair negative 4, 4, b at negative 2, 2, c at negative 2, negative 1, d at negative 4, 1. figure a prime b prime c prime d prime has a prime at ordered pair 3, negative 4, b prime at 5, negative 2, c prime at 5, 1, d prime at 3, negative 1.

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)

A).  To go from ABCD to A'B'C'D' takes two transformations.

Step-1 :  Reflect the original figure around the x-axis.

Step-2 :  Slide the new figure 7 units to the right.

See the attached drawing.  It shows the whole process
including the intermediate status and coordinates of
the four points after Step-1.  You'll love it.

B).  I looked up a definition of 'congruent'.   It said that two figures
are congruent if they have have the same shape and size after
being moved, rotated, or reflected.  (I was worried about the
'reflected' part.)

With that definition, I'll let you decide whether these figures
are congruent.

In conclusion, let me express my gratitude for the generous
5-points bounty with which I've been showered by answering
this question.  The green crust and the cup of tepid turgid water
have been delicious, and by working quickly and efficiently, I was
able to construct the attached file in less than an hour.

Part One:

Reflection over the y-axis and vertical translation 3 units down.

Part Two:

The two figures are congruent, they are the same shape and size.