Question

Which of the following shows why trapezoid ABCD is congruent to trapezoid

A'B'C'D?
O
A) The trapezoid was reflected across the x-axis and shifted 7 units in the x
direction and -3 units in the y direction.
O
B) The trapezoid was reflected across the y-axis and shifted 6 units in the y
direction
O
C) The trapezoid was reflected across the x-axis and shifted - 3 units in the x
direction and 7 units in the y direction
D) the trapezoid was shifted 7 units in the x direction and 6 units in the y direction

Answer 1

The Answer c explanation

Answer 2

The correct answer is option D. The trapezoid was shifted 7 units in the x-direction and 6 units in the y-direction.

To determine the transformation that makes trapezoid ABCD congruent to trapezoid A'B'C'D, we need to analyze the change in position. Let's consider the original positions of corresponding vertices and the possible transformations:

Original vertices:

- A(-5, -4)

- B(-5, -5)

- C(-2, -5)

- D(-3, -4)

Corresponding vertices:

- A'(2, 1)

- B'(2, 2)

- C'(5, 2)

- D'(4, 1)

Now let's analyze the transformations in each option:

A) Reflected across the x-axis and shifted 7 units in the x-direction and -3 units in the y-direction:

- This involves reflection and translation, not congruent.

B) Reflected across the y-axis and shifted 6 units in the y-direction:

- This involves reflection and translation, not congruent.

C) Reflected across the x-axis and shifted -3 units in the x-direction and 7 units in the y-direction:

- This involves reflection and translation, not congruent.

D) Shifted 7 units in the x-direction and 6 units in the y-direction:

- This involves translation, which preserves shape and size, making the trapezoid congruent.

Therefore, the correct option is D. The trapezoid was shifted 7 units in the x-direction and 6 units in the y-direction.