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The rule (x,y)→(−x,y) maps △ABC to △A′B′C′.


Which statement correctly describes the relationship between △ABC and △A′B′C′ ?


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 △A′B′C′

is a reflection of △ABC, and a reflection 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.


The triangles are not congruent because △A′B′C′

is a reflection of △ABC, and a reflection is not a rigid motion.

Verified Answer :

Going from (x,y) to (-x,y) is telling us we have a reflection going on. For example, (1,2) will map to (-1,2). This is a reflection over the y axis (the vertical axis). A reflection will keep two points the same distance apart. So it preserves distances and side lengths. Therefore, if ABC is reflected over the y axis then A'B'C' is congruent to ABC. 

The final answer is choice B.

The correct option is :

(B)The triangle are congruent because the triangle A'B'C' is a reflection of triangle ABC and a reflection is a rigid motion.

Step-by-step explanation:

Given information:

The rule (x,y) going to (-x,y) maps triangle ABC to Triangle A'B'C'

Now,

The reflection is going on if we are going from (x,y) to (-x,y)

For example the point (1,3) will map (-1,3) , this is a reflection over y axis.

A reflection will keep the two points the same distance apart so we can say it will preserve the side length and distance.

Hence, if triangle ABC is reflected over y axis then A'B'C' is congruent to ABC.

So, The correct option is :

(B)The triangle are congruent because the triangle A'B'C' is a reflection of triangle ABC and a reflection is a rigid motion.

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