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′? responses △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. triangle a b c, is congruent to , triangle a prime b prime c prime, because you can map , triangle a b c, to , triangle a prime b prime c prime, using a reflection across the , x, -axis followed by a translation 3 units down, 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. triangle a b c, is congruent to , triangle a prime b prime c prime, because you can map , triangle a b c, to , triangle a prime b prime c prime, using a translation 3 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′. triangle a b c, is not congruent to , triangle a prime b prime c prime, because there is no sequence of rigid motions that maps , triangle a b c, to , triangle a prime b prime c prime, . △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.

Answer 1

△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:

The statement that correctly describes the relationship between △ABC and △A'B'C' 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.

To demonstrate congruence, we can perform a reflection across the x-axis to change the y-coordinates of the vertices. This transformation will map A(-1, 1) to A'(-1, -4), B(-2, 3) to B'(-2, -6), and C(-5, 1) to C'(-5, -4). Then, we can perform a translation 3 units down to map A' to A'(-1, -4+3), B' to B'(-2, -6+3), and C' to C'(-5, -4+3). The resulting coordinates of the vertices of △A'B'C' will be A'(-1, -1), B'(-2, -3), and C'(-5, -1), which are equal to the original coordinates of △ABC.