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# Congruence and rigid motion

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The coordinates of the vertices of △ABC are A(−1, 1) , B(−2, 3) , and C(−5, 1) . The coordinates of the vertices of △A′B′C′ are A′(−1, −4) , B′(−2, −6) , and C′(−5, −4) .

Which statement correctly describes the relationship between △ABC and △A′B′C′ ?

△ABC is congruent to △A′B′C′ because you can map △ABC to △A′B′C′ using a translation 5 units down followed by a reflection across the x-axis, which is a sequence of rigid motions.

△ABC is congruent to △A′B′C′ because you can map △ABC to △A′B′C′ using a translation 3 units down followed by a reflection across the x-axis, which is a sequence of rigid motions.

△ABC is congruent to △A′B′C′ because you can map △ABC to △A′B′C′ using a reflection across the x-axis followed by a translation 3 units down, which is a sequence of rigid motions.

△ABC is not congruent to △A′B′C′ because there is no sequence of rigid motions that maps △ABC to△A′B′C′ .

Oct 18, 2018

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If B'  were (-2, -2)...... A'B'C'  would be  ABC  translated down 5  units...but since  B' = (-2,- 6)

There is no sequence of rigid motions that maps  ABC to A'B'C'    [ last answer ]   Oct 18, 2018