Question

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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. (6 points)

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

Answer 1

A. first you can translate the lines 4 squares down.

then reflect the figure on th y line.

(attention: the rotation cant be done.)

B. yes they are. although we translated and reflected the figure l, we did not make any kind of change in size

good luck

Answer 2

Part A: The graph reflected across y-axis and translated 4 units down.

Part B: Yes both figures are congruent.

Explanation:

Part A:

From the given figure it is clear that the vertices of preimage are A(-4,4), B(-2,2), C(-2,-1) and D(-4,1).

The vertices of image are A'(4,0), B'(2,-2), C'(2,-5) and D'(4,-4).

The relation between preimage and image is defined by the rule

`(x,y)\rightarrow (-x,y-4)`

The graph reflected across y-axis, so

`(x,y)\rightarrow (-x,y)`

then translated 4 units down.

`(x,y)\rightarrow (-x,y-4)`

Therefore the graph of figure ABCD reflected across y-axis and translated 4 units down to get A'B'C'D'.

Part B:

Reflection and translation are rigid transformation. It means the size and shape of the image is same after reflection and translation.

Rigid transformation always produce congruent figures.

Since figure ABCD reflected across y-axis and translated 4 units down to get A'B'C'D', therefore

`ABCD\cong A'B'C'D'`

Yes both figures are congruent.