Question

△JKL is mapped to △J'K'L' using the rules (x, y)→(x+2, y+3) followed by (x, y)→(2x, y) .

Which statement describes the relationship between △JKL and △J'K'L'?

A △JKL is not congruent to △J'K'L' because the rules do not represent a sequence of rigid motions.
B △JKL is congruent to △J'K'L' because the rules represent a rotation followed by a reflection, which is a sequence of rigid motions.
C △JKL is congruent to △J'K'L' because the rules represent a translation followed by a reflection, which is a sequence of rigid motions.
D △JKL is congruent to △J'K'L' because the rules represent a translation followed by a rotation, which is a sequence of rigid motions.

Answer 1

Answer:

A. ΔJKL is not congruent to ΔJ'K'L' because the rules do not represent a sequence of rigid motions.

Step-by-step explanation:

ΔJKL is mapped to ΔJ'K'L' using the rules $(x, y)\rightarrow (x+2, y+3)$ followed by $(x, y)\rightarrow (2x, y)$

From geometry we know while rotating, reflecting and translating the size of the figure remains as it is, so they are congruent.

But in case of dilation the figure gets resized i.e their size gets changed. So they are similar not congruent.

In this case, first the triangle goes under $(x, y)\rightarrow (x+2, y+3)$ i.e 2 units translated to right and 3 units translated to up.

But after then it undergoes $(x, y)\rightarrow (2x, y)$, where it undergoes a dilation of factor 2, so it is no more congruent to the original figure.

Answer 2

Answer:

△JKL is not congruent to △J′K′L′ because there is no sequence of rigid motions that maps △JKL to △J′K′L′.