Question

The coordinates of the vertices of trapezoid JKLM are J(2, −3) , K(6, −3) , L(4, −5) , and M(1, −5) . The coordinates of the vertices of trapezoid J′K′L′M′ are J′(−3, 3) , K′(−3, 7) , L′(−5,  5) , and M′(−5,  2) . Which statement correctly describes the relationship between trapezoid JKLM and trapezoid J′K′L′M′ ?
 Trapezoid JKLM is not congruent to trapezoid J′K′L′M′ because there is no sequence of rigid motions that maps trapezoid JKLM to trapezoid J′K′L′M′ .

Trapezoid JKLM is congruent to trapezoid J′K′L′M′ because you can map trapezoid JKLM to trapezoid J′K′L′M′ by reflecting it across the line y = x and then translating it 1 unit up, which is a sequence of rigid motions.

 Trapezoid JKLM is congruent to trapezoid J′K′L′M′ because you can map trapezoid JKLM to trapezoid J′K′L′M′ by rotating it 180° about the origin and then translating it 1 unit down, which is a sequence of rigid motions.

Trapezoid JKLM is congruent to trapezoid J′K′L′M′ because you can map trapezoid JKLM to trapezoid J′K′L′M′ by reflecting it over the x-axis and then over the line y = x, which is a sequence of rigid motions.

Answer 1

This is your answer:
Trapezoid JKLM is congruent to trapezoid J′K′L′M′ because you can map trapezoid JKLM to trapezoid J′K′L′M′ by reflecting it across the line y = x and then translating it 1 unit up, which is a sequence of rigid motions.

Answer 2

Answer:

Option b is right.

Step-by-step explanation:

We are given that the coordinates of the vertices of trapezoid JKLM are J(2, −3) , K(6, −3) , L(4, −5) , and M(1, −5)

and that of  J′K′L′M′ are J′(−3, 3) , K′(−3, 7) , L′(−5,  5), and M′(−5,  2) .

On comparing the coordinates we find that y coordinates of JKLM vertices have become x coordinates of J'K'L'M'.

So there was a reflection of the vertices about the line y =x.

Because of this reflection we get nw coordinates as

(−3, 2) , (−3, 6) , L′(−5,  4), and M′(−5,  1) .

Again there was a shift of 1 unit of y i.e. vertical shift of 1 unit up.

Hence new coordinates would be

J′(−3, 3) , K′(−3, 7) , L′(−5,  5), and M′(−5,  2)

Thus we find that new trapezium is congruent to original trapezium

Correct option is

Trapezoid JKLM is congruent to trapezoid J′K′L′M′ because you can map trapezoid JKLM to trapezoid J′K′L′M′ by reflecting it across the line y = x and then translating it 1 unit up, which is a sequence of rigid motions.