Question

The rule (x,y)→(−x,−y)(x,y)→(−x,−y) maps △RST△RST to △R′S′T′△R′S′T′.

Which statement correctly describes the relationship between △RST△RST and △R′S′T′△R′S′T′ ?

The triangles are congruent because △R′S′T′△R′S′T′ is a translation of △RST△RST , and a translation is a rigid motion.

The triangles are congruent because △R′S′T′△R′S′T′ is a rotation of △RST△RST , and a rotation is a rigid motion.

The triangles are not congruent because △R′S′T′△R′S′T′ is a rotation of △RST△RST , and a rotation is not a rigid motion.

The triangles are not congruent because △R′S′T′△R′S′T′ is a translation of △RST△RST , and a translation is not a rigid motion.

Answer 1

The triangles are congruent because △R′S′T′ is a translation of△RST , and a translation is a rigid motion.

Explanation:

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Answer 2

The correct option is 2. The triangles are congruent because △R′S′T′ is a rotation of △RST, and a rotation is a rigid motion.

Explanation:

It is given that △RST maps to △R′S′T′ by using the rule

`(x,y)\rightarrow (-x,-y)`

Since the absolute values of x and y-coordinates are same but the sign of both coordinates are changed. It is possible, if the figure is rotated 180 degree about the origin.

When a figure rotated 180 degree about the origin, then

`(x,y)\rightarrow (-x,-y)`

Rotation is a rigid motion and image and preimage are congruent to each other.

Therefore option 2 is correct.