Question

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 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 translation 5 units down followed by a reflection across the x-axis, 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′ .
△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.

Answer 1

Check the picture.

Note that reflecting triangle ABC with respect to the x-axis, and translating it 3 units down, mapps it perfectly to A'B'C'.


Thus, the answer is: △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.

Answer 2

Answer:

△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.

Step-by-step explanation:

I took the test/ other answer is somewhat correct