Question

The coordinates of the vertices of trapezoid ABCD are A (2,6), B (5,6), C (7,1), and D (-1,1). The coordinates of the vertices of trapezoid A'B'C'D' are A' (-6, -2),B' (-6, -5), C' (-1, -7), and D' (-1, 1). Which statement correctly describes the relationship between trapezoid ABCD and trapezoid A'B'C'D' ?

A. Trapezoid ABCD ≅ trapezoid A'B'C'D'
You can reflect trapezoid ABCD across the x-axis and then across the y-axis.


B. Trapezoid ABCD ≅ trapezoid A'B'C'D'
You can rotate trapezoid ABCD 180°about the origin and then translating it 4 units left.


C. Trapezoid ABCD ≅ trapezoid A'B'C'D'
You can reflect trapezoid ABCD across the x-axis and then rotating it 90°clockwise.

Answer 1

C. Trapezoid ABCD ≅ trapezoid A'B'C'D'

You can reflect trapezoid ABCD across the x-axis and then rotating it 90°clockwise.

Explanation:

Given : The coordinates of the vertices of trapezoid ABCD are A (2,6), B (5,6), C (7,1), and D (-1,1). The coordinates of the vertices of trapezoid A'B'C'D' are A' (-6, -2),B' (-6, -5), C' (-1, -7), and D' (-1, 1).

To find : Which statement correctly describes the relationship between trapezoid ABCD and trapezoid A'B'C'D'.

Solution : We have given that trapezoid ABCD.

Parent coordinates of A (2,6), B (5,6), C (7,1), and D (-1,1)

Translated coordinates A' (-6, -2),B' (-6, -5), C' (-1, -7), and D' (-1, 1).

By reflection rule : Reflection across x axis (x , y) →→( x , -y) and rotating it 90°clockwise (x , y) →→( -y, x).

Therefore, C. Trapezoid ABCD ≅ trapezoid A'B'C'D'

You can reflect trapezoid ABCD across the x-axis and then rotating it 90°clockwise.

Answer 2

Correct answer is option C.

Explanation:

Trapezoid ABCD ≅ trapezoid A'B'C'D'

You can reflect trapezoid ABCD across the x-axis and then rotating it 90°clockwise.