Question

which of the following sequences of transformations maps △mno onto △abc?

sequence a
a translation along the directed line segment \\(\overline{nb}\\), then a reflection over the vertical line through point b.

sequence b
a reflection over the vertical line \\(\overleftrightarrow{mo}\\), then a translation along the directed line segment \\(\overline{mb}\\).

choose 1 answer:
\\(\boldsymbol{\text{a}}\\) only sequence a
\\(\boldsymbol{\text{b}}\\) only sequence b
\\(\boldsymbol{\text{c}}\\) both
\\(\boldsymbol{\text{d}}\\) neither

Explanation:

Step1: Analyze Sequence A

First, translate \( \triangle MNO \) along \( \overline{NB} \), which moves \( N \) to \( B \). Then reflect over the vertical line through \( B \). This should align \( \triangle MNO \) with \( \triangle ABC \) if the shapes are congruent and orientations match.

Step2: Analyze Sequence B

Reflect \( \triangle MNO \) over vertical line \( \overleftrightarrow{MO} \), then translate along \( \overline{MB} \). This also can map \( \triangle MNO \) to \( \triangle ABC \) as reflections and translations preserve congruence and can align the triangles.

Step3: Compare Sequences

Both sequences use rigid transformations (translation, reflection) which preserve the shape and size, so both can map \( \triangle MNO \) onto \( \triangle ABC \).

Answer:

C. Both