Question

△RST is mapped to △R′S′T′ using the rule (x, y)→(x, −y) followed by (x, y)→(3x, 3y) .

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

△RST is congruent to △R′S′T′ because the rules represent a reflection followed by a rotation, which is a sequence of rigid motions.

△RST is congruent to △R′S′T′ because the rules represent a reflection followed by a translation, which is a sequence of rigid motions.

△RST is congruent to △R′S′T′ because the rules represent a rotation followed by a translation, which is a sequence of rigid motions.

△RST is not congruent to △R′S′T′ because the rules do not represent a sequence of rigid motions.

By the way, this question DOES NOT include a picture, so don't ask please.

Answer 1

△RST is not congruent to △R′S′T′ because the rules do not represent a sequence of rigid motions.

Explanation:

Answer 2

The rule (x,y) --> (x,-y) reflects the triangle over the x axis. So far the triangle has not changed size at all. So the triangles are congruent.

However, when we use (x,y) --> (3x,3y), the triangle will get larger. Now the triangle is no longer congruent to the original.

So the answer is choice D.

When they mention "rigid motions" they mean reflections and translations (aka vertical/horizontal shifts). Dilations are not rigid motions. They do not preserve size.