Question

The rule (x,y)→(−x,y) maps △abcto △a′b′c′. which statement correctly describes the relationship between △abcand △a′b′c′? responses the triangles are congruent because △a′b′c′ is a reflection of △abc , and a reflection is a rigid motion. the triangles are congruent because , triangle a prime b prime c prime, is a reflection of , triangle a b c, , and a reflection is a rigid motion. the triangles are not congruent because △a′b′c′ is a reflection of △abc, and a reflection is not a rigid motion. the triangles are not congruent because , triangle a prime b prime c prime, is a reflection of , triangle a b c, , and a reflection is not a rigid motion. the triangles are congruent because △a′b′c′ is a rotation of △abc, and a rotation is a rigid motion. the triangles are congruent because , triangle a prime b prime c prime, is a rotation of , triangle a b c, , and a rotation is a rigid motion. the triangles are not congruent because △a′b′c′ is a translation of △abc, and a translation is not a rigid motion.

Answer 1

The correct statement is that the triangles are congruent because △a'b'c' is a reflection of △abc, and a reflection is a rigid motion.

Step-by-step explanation:

The transformation rule (x,y)→(−x,y) describes a reflection over the y-axis. When △abc is transformed using this rule to become △a'b'c', each point of the original triangle is reflected across the y-axis to its mirror image position. This reflection is considered a rigid motion, which means that the size and shape of the triangle remain unchanged, although the triangle may be flipped or reoriented in some way.

Therefore, the correct statement describing the relationship between △abc and △a'b'c' is: The triangles are congruent because △a'b'c' is a reflection of △abc, and a reflection is a rigid motion.