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′?

Responses

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′.
trapezoid E F G H is not congruent to trapezoid E prime F prime G prime H prime because there is no sequence of rigid motions that maps trapezoid E F G H to trapezoid E prime F prime G prime H prime .

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.
trapezoid E F G H is congruent to trapezoid E prime F prime G prime H prime because you can map trapezoid E F G H to trapezoid E prime F prime G prime H prime by dilating it by a factor of 3 fourths and then translating it 2 units left, which is a sequence of rigid motions.

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.

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

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

Answer 1

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

Reason: corresponding side EH = 4 while E′H′ = 3 (and FG = 12 while F′G′ = 9), so side lengths are not equal. The vertices satisfy E′ = (3/4)E + (−2,0), etc., so the map from EFGH to E′F′G′H′ is a dilation by factor 3/4 followed by a translation 2 units left — not a rigid motion — hence the trapezoids are not congruent.