Question

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

Part B: Are the two figures congruent? Explain your answer

Answer 1

Answer:

The coordinates of the figure = A' (4,1) ,B'(2,-1) , C' (2,-4) , D'(4,-2) , A(-4,4 , B (-2,2 ) , C (-2,-2) , D(-4,1 )

Yes both are congurant to each other.

Answer 2

Given : figure ABCD to figure A′B′C′D′.

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

Solution:

A (- 4 , 4)  , A' ( 4 , 1)

B ( -2 , 2)  , B' ( 2 , - 1)

C ( -2 , - 1) , C' ( 2 , - 4)

D ( -4 , 1 )   , D' ( 4 , - 2)

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

3 step down

Y = y - 3

(x , y) →  (x , y - 3)

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

 (  2 , 2)→ B' ( 2 , - 1)    ∵( 2 - 3 = -1)

 (  2 , - 1)→ C' ( 2 , - 4)   ∵ ( -1 - 3 = -4)

 (  4 , 1 ) → D' ( 4 , - 2)  ∵  (1 - 3 = -2)

(x , y) →  (-x , y - 3)  ( overall transformation )

Two figures are congruent

as there is no scaling done  

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