Rectangle ABCD has points at A (4, −2), B(4, 4), C(8, 4), and D(8, −2). After undergoing a transformation, its new points are A'(2, −1), B'(2, 2), C'(4, 2), and D (4, −1). Is the new figure congruent to the old figure? Why or why not?

The new figure is not congruent with the old figure. They are similar

Step-by-step explanation:

Transformations

We are given the vertices of rectangle ABCD and the vertices of rectangle A'B'C'D'.

It can be clearly noted all the coordinates of the second rectangle are half the value of the coordinates of the first rectangle.

This type of transformation corresponds to a dilation across the origin with a scale factor of 1/2.

Since the transformed rectangle is smaller than the first one, it cannot be congruent with it.

But since all the dimensions of this smaller rectangle are proportional to those of the bigger rectangle, they are similar.

step by step solution :

step   1   :

1.1     4 = 22

(4)3 = (22)3 = 26

equation at the end of step   1   :

  ((23) • 26)2

step   2   :

equation at the end of step   2   :

  (23 • 26)2

step   3   :

final result :

  218

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