Question

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 a. reflect xyz across line ac. 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 b. reflect xyz across line cb.

Explanation:

Step1: First, translation

Translate $\triangle XYZ$ along $\overrightarrow{YC}$ to get a new - positioned triangle $\triangle X'Y'Z'$. This moves $\triangle XYZ$ to the general area of $\triangle BCA$.

Step2: Then, rotation

Rotate $\triangle X'Y'Z'$ about point $C$ so that $X'$ coincides with $B$. This starts to align the vertices of the two triangles.

Step3: Finally, reflection

Reflect the rotated triangle $\triangle X''Y''Z''$ across line $AC$. After this reflection, $\triangle XYZ$ will coincide with $\triangle BCA$.

Answer:

B. 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 AC.