we have the coordinates
A(-4,4)
B(-2,2)
C(-2,-1)
D(-4,1)
step 1
First transformation
Translation of the figure ABCD 1 unit up
The rule is
(x,y) --------> (x,y+1)
Applying the rule
A(-4,4) -----------> A''(-4,5)
B(-2,2) ---------> B''(-2,3)
C(-2,-1) -------> C''(-2,0)
D(-4,1) ------> D''(-4.2)
step 2
Reflection over the x-axis
The rule is
(x,y) ------> (x,-y)
Applying the rule
A''(-4,5) -------> A'''(-4,-5)
B''(-2,3) ------> B'''(-2,-3)
C''(-2,0) -----> C'''(-2,0)
D''(-4.2) -----> D'''(-4,-2)
step 3
Third transformation
Translation 7 units to the right and 1 unit up
(x,y) ------> (x+7,y+1)
Applying the rule
A'''(-4,-5) ---------> A'(3,-4) is ok
B'''(-2,-3) ---------> B'(5,-2) is ok
C'''(-2,0) ---------> C'(5,1) is ok
D'''(-4,-2) ------> D'(3,-1) is ok
Part B
Remember that
The rigid transformations produce congruent figures
The rigid transformations are: rotation, reflection, and translation
In this problem the transformations are rigid
that means
The pre-image and the final image are congruent