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′ ?

A.) △RST is not congruent to △R′S′T′ because the rules do not represent a sequence of rigid motions.
B.) △RST is congruent to △R′S′T′ because the rules represent a rotation followed by a translation, which is a sequence of rigid motions.
C.) △RST is congruent to △R′S′T′ because the rules represent a reflection followed by a rotation, which is a sequence of rigid motions.
D.) △RST is congruent to △R′S′T′ because the rules represent a reflection followed by a translation, which is a sequence of rigid motions.

Answer 1

a is the correct answer

Explanation:

Answer 2

Remember:

a) (x,y) => (x, -y) is a reflection across X axis

b) (x,y) => (-x,y) is a reflection across Y axis

Here △RST is mapped to △R′S′T′ using the rule (x,y)→(x,−y)

Hence it is a reflection across X axis.

The size of the triangle does not alter.

But when this is followed by (x,y)→(3x,3y), the lengths increase by a factor 3.

Hence the triangles do not remain congruent.

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

Option A) is the right answer