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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 is not congruent to trapezoid A′B′C′D′ because there is no sequence of rigid motions that maps trapezoid ABCD to trapezoid A′B′C′D′ .

b) Trapezoid ABCD is congruent to trapezoid A′B′C′D′ because you can map trapezoid ABCD to trapezoid A′B′C′D′ by reflecting it across the x-axis and then across the y-axis, which is a sequence of rigid motions.

c) Trapezoid ABCD is congruent to trapezoid A′B′C′D′ because you can map trapezoid ABCD to trapezoid A′B′C′D′ by reflecting it across the x-axis and then rotating it 90° clockwise, which is a sequence of rigid motions.


d) Trapezoid ABCD is congruent to trapezoid A′B′C′D′ because you can map trapezoid ABCD to trapezoid A′B′C′D′ by rotating it 180° about the origin and then translating it 4 units left, which is a sequence of rigid motions.

Respuesta :

Answer:

I think it is D but i could be wrong


Step-by-step explanation:

When the shape and size of the two figure is same then they are called as congruent shape. The option C is the correct option.

Given information-

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) .

What is congruent shape?

When the shape and size of the two figure is same then they are called as congruent shape.

Let check the statements,

  • A) As the shape and size of the trapezoid A′B′C′D′ is equal to the trapezoid ABCD . Thus both are congruent and this statement is incorrect.

  • B) As by reflecting the trapezoid ABCD  across the x-axis gives the point (-1,-1) for vertices of A. Now by reflecting the trapezoid ABCD across the y-axis gives the point (-1,1) for vertices of A. Which is not equal to the vertices of A'(-6,2). Thus this is incorrect statement.

  • C) As by reflecting the trapezoid ABCD  across the x-axis gives the point (2,-6) for vertices of A. Now by rotating the trapezoid ABCD 90 degreee clockwise gives the point (-6,-2) for vertices of A. Which is equal to the vertices of A'(-6,2). This can be true for all the points. Thus this is correct statement.

Hence the option C is the correct option.

Learn more about the congruent shape here;

https://brainly.com/question/24430586

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