BRAINLIEST 25 POINTS 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)

Step-by-step explanation:

To Find :  Write the sequence of transformations that changes figure ABCD to figure A′B′C′D′.

Solution:

A (- 4 , 4)  , A' ( 4 ,  0)

B ( -2 , 2)  , B' ( 2 , - 2)

C ( -2 , - 1) , C' ( 2 , - 5)

D ( -4 , 1 )   , D' ( 4 , - 3)

1st Transformation  - reflection across y axis  

=> sign of x coordinate gets changed

(x , y) → ( -x , y)

A (- 4 , 4)  →  ( 4 , 4)

B ( -2 , 2) →  ( 2 , 2)

C ( -2 , - 1) →   ( 2 , - 1)

D ( -4 , 1 )  →   ( 4 , 1)

2nd transformation

4 step down

Y = y - 0

(x , y) →  (x , y - 3)

(  4 , 4) → A' ( 4 , 0)  ∵ ( 4 - 4 = 0)

(  2 , 2)→ B' ( 2 , - 2)    ∵( 2 - 4 = -2)

(  2 , - 1)→ C' ( 2 , -5)   ∵ ( -1 - 4 = -5)

(  4 , 1 ) → D' ( 4 , - 3)  ∵  (1 - 4 = -3)

(x , y) →  (-x , y -4)  ( overall transformation )

Two figures are congruent

as there is no scaling done  

To Find :  Write the sequence of transformations that changes figure ABCD to figure A′B′C′D′.

Solution:

A (- 4 , 4)  , A' ( 4 ,  0)

B ( -2 , 2)  , B' ( 2 , - 2)

C ( -2 , - 1) , C' ( 2 , - 5)

D ( -4 , 1 )   , D' ( 4 , - 3)

1st Transformation  - reflection across y axis  

=> sign of x coordinate gets changed

(x , y) → ( -x , y)

A (- 4 , 4)  →  ( 4 , 4)

B ( -2 , 2) →  ( 2 , 2)

C ( -2 , - 1) →   ( 2 , - 1)

D ( -4 , 1 )  →   ( 4 , 1)

2nd transformation

4 step down

Y = y - 0

(x , y) →  (x , y - 3)

(  4 , 4) → A' ( 4 , 0)  ∵ ( 4 - 4 = 0)

(  2 , 2)→ B' ( 2 , - 2)    ∵( 2 - 4 = -2)

(  2 , - 1)→ C' ( 2 , -5)   ∵ ( -1 - 4 = -5)

(  4 , 1 ) → D' ( 4 , - 3)  ∵  (1 - 4 = -3)

(x , y) →  (-x , y -4)  ( overall transformation )

Two figures are congruent

as there is no scaling done  

Step-by-step explanation: