Question

The rule (x,y)→(−x,−y) maps △RST to △R′S′T′. Which statement correctly describes the relationship between △RST and △R′S′T′?ResponsesThe triangles are congruent because △R′S′T′ is a translation of△RST , and a translation is a rigid motion.The triangles are congruent because , triangle R prime S prime T prime, is a translation of, triangle R S T, , and a translation is a rigid motion.The triangles are not congruent because △R′S′T′ is a rotation of△RST , and a rotation is not a rigid motion.The triangles are not congruent because , triangle R prime S prime T prime, is a rotation of, triangle R S T, , and a rotation is not a rigid motion.The triangles are not congruent because △R′S′T′ is a translation of△RST , and a translation is not a rigid motion.The triangles are not congruent because , triangle R prime S prime T prime, is a translation of, triangle R S T, , and a translation is not a rigid motion.The triangles are congruent because △R′S′T′ is a rotation of△RST , and a rotation is a rigid motion.

Answer 1

The correct relationship between △RST and △R'S'T' is that the triangles are congruent because △R'S'T' is a reflection of △RST, and a reflection is a type of rigid motion that preserves distances and angles.

Step-by-step explanation:

The rule (x,y)→(−x,−y) reflects each point of △RST over the origin to create △R'S'T'. This type of transformation is known as a reflection, which is a specific type of rigid motion. A rigid motion is a transformation that preserves distances and angles, meaning the pre-image and the image are congruent.

Therefore, the correct statement describing the relationship between △RST and △R'S'T' is that the triangles are congruent because △R'S'T' is a reflection of △RST, and a reflection is a rigid motion. This transformation is neither a translation nor a rotation; in a translation, all points of the figure move the same distance in the same direction, and in a rotation, all points move around a central point at a certain angle, but their distances to the central point remain constant.