Question

The coordinates of the vertices of trapezoid EFGH are E(-8, 8), F(-4, 12), G(-4, 0), and H(-8, 4).  The coordinates of the vertices of trapezoid E’F’G’H’ are E’(-8, 6), F’(-5, 9), G’(5, 0), and H’(-8, 3).

 

Which statement correctly describes the relationship between trapezoid EFGH and trapezoid E’F’G’H’?

 

a)     Trapezoid EFGH is congruent to trapezoid E’F’G’H’ because you can map trapezoid EFGH to trapezoid E’F’G’H’ by reflecting it across the x-axis and then translating it up 14 units, which is a sequence of rigid motions.

b)     Trapezoid EFGH is congruent to trapezoid E’F’G’H’ because you can map trapezoid EFGH to trapezoid E’F’G’H’ by translating it down 2 units and then reflecting it over the y-axis, which is a sequence of rigid motions

c)     Trapezoid EFGH is congruent to trapezoid E’F’G’H’ because you can map trapezoid EFGH to trapezoid E’F’G’H’ by dilating it by a factor of 34 and then translating it 2 units left, which is a sequence of rigid motions

d) Trapezoid EFGH is not congruent to trapezoid E’F’G’H’ because there is no sequence of rigid motions that map trapezoid EFGH to trapezoid E’F’G’H’.

Answer 1

D. Trapezoid EFGH is not congruent to trapezoid E'F'G'H' because there is no sequence of rigid motions that maps trapezoid EFGH to trapezoid E'F'G'H'

Explanation:

I just took the test! & btw, the other guy's graph is wrong, but his answer is not. Good luck guys & girls!

Answer 2

D

Explanation:

1) We have and isosceles trapezoid DEFG and and another trapezoid D'E'F'G' dilated.

2) E'F'G'H' is not congruent to EFGH (due to its legs) Besides that, E'F'G'H has undergone not to rigid motions. Rigid motions are better known as translations and rotations and they preserve length and angles. That was not the case.

(Check graph 2)

3) So it's d, the only correct choice:

d) Trapezoid EFGH is not congruent to trapezoid E’F’G’H’ because there is no sequence of rigid motions that map trapezoid EFGH to trapezoid E’F’G’H’.