Question

I NEED THIS ASAP!!!!!!
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

Part A: Reflection over y-axis then translate 4 units down. After reflection a= (4,4), b=(2,2), c=(2,-1), d=(4,1). After the translation the end points are the ones shown in the end product.
Part B: yes the are congruent bc they are the same shape, have same lengths. They’re the exact same size

Answer 2

Part A: (x, y) ⇒ (x, y -3) is the overall transformation

Part B: Yes both figures are congruent.

What is transformation?

A transformation is a process that manipulates a polygon or other two-dimensional object on a plane or coordinate system.

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'(4,1), B'(2,-1), C'(2,-4) and 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, 4 - 3) = (4, 1)

(2, 2) ⇒ B'(2, 2 - 3) = (2, -1)

(2, -1) ⇒ C'(2, -1 - 3) = (2, -4)

(4, 1) ⇒ D'(4, 1 - 3) = (4, -2)

(x, y) ⇒ (-x, y -3) is the overall transformation

Part B:

Two figures are congruent because they have same size and shape.

Find out more information about transformation here

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