Question

1. the triangles are congruent. which sequence of rigid motions will take triangle xyz onto triangle bca?

a. translate xyz using directed line segment yc. rotate xyz using c as the center so that x coincides with b. reflect xyz across line cb.
b. translate xyz using directed line segment yc. rotate xyz using c as the center so that x coincides with b. reflect xyz across line ac.
c. translate xyz using directed line segment yc. rotate xyz using c as the center so that x coincides with a. reflect xyz across line cb.
d. translate xyz using directed line segment yc. rotate xyz using c as the center so that x coincides with a. reflect xyz across line ac.

Explanation:

Step1: Analyze translation

Translate \( XYZ \) using directed line segment \( YC \). This moves the triangle to a new position relative to point \( C \).

Step2: Analyze rotation

Rotate \( X'Y'Z' \) using \( C \) as the center so that \( X'' \) coincides with \( B \). This aligns a vertex with the target triangle's vertex.

Step3: Analyze reflection

Reflect \( X''Y''Z'' \) across line \( CB \). This final transformation maps the triangle \( XYZ \) onto triangle \( BCA \).

Answer:

A. Translate \( XYZ \) using directed line segment \( YC \). Rotate \( X'Y'Z' \) using \( C \) as the center so that \( X'' \) coincides with \( B \). Reflect \( X''Y''Z'' \) across line \( CB \).