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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′ ?

 

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.

 

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.

 

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.

 

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′ .

cedes  Mar 6, 2018
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Not the first option  because  reflecting D =  (- 1, 1)   across the x  axis produces (-1,-1)  and  reflecting this across the y axis produces  ( 1, - 1)   which isn't  D'

 

Not he second option  because    rotating  D =  (-1, 1)  180°   about thhhe origin produces ( 1, - 1)....shifting this 4 units too the left produces  ( -3, -1)  which isn't  D'

 

Third  option because  

 (2, 6)  across x  ⇒ (2, - 6) ⇒ 90° clockwise ⇒  (-6, -2)  = A'

(5, 6)  across x   ⇒ (5, -6)  ⇒ 90° clockwise ⇒ (-6, - 5) = B'

(7, 1) across x ⇒ (7, - 1)  ⇒ 90° clockwise ⇒  (-1, -7) = C'

( - 1, 1)  across x ⇒ ( -1, - 1) ⇒ 90° clockwise ⇒ (-1, 1) = D'

 

 

cool cool cool

CPhill  Mar 6, 2018

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