Question

3 practice 3
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

First, we need to translate \( \triangle XYZ\) using the directed line segment \( YC\). This moves the triangle so that \( Y\) coincides with \( C\).

Step2: Analyze rotation

Next, rotate \( \triangle X''Y''Z''\) (after translation) around \( C\) as the center. The goal is to make \( X''\) coincide with \( B\).

Step3: Analyze reflection

Finally, reflect \( \triangle X'''Y'''Z'''\) (after rotation) across line \( CB\). This will map \( \triangle XYZ\) 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 \( CB\).