2. in the diagram, figure e is congruent to figure d. which sequences of rigid motions describe how to map one figure onto the other? choose all that apply.
a. a translation along $ \overrightarrow { a b } $ followed by a reflection across line $ \ell $ maps figure e onto figure d.
b. a translation along $ \overrightarrow { b a } $ followed by a reflection across line $ \ell $ maps figure d onto figure e.
c. a reflection across line $ \ell $ followed by a translation along $ \overrightarrow { a b } $ maps figure e onto figure d.
d. a reflection across line $ \ell $ followed by a translation along $ \overrightarrow { b a } $ maps figure e onto figure d.
e. a reflection across line $ \ell $ followed by a translation along $ \overrightarrow { b a } $ maps figure d onto figure e.

Question

Accepted Answer

# Explanation:
## Step1: Analyze Option A
A translation along $\overrightarrow{AB}$ moves figure $E$ left - ward (since $\overrightarrow{AB}$ is from $A$ to $B$). Then a reflection across line $\ell$ would not map figure $E$ onto figure $D$.
## Step2: Analyze Option B
A translation along $\overrightarrow{BA}$ moves figure $D$ right - ward (since $\overrightarrow{BA}$ is from $B$ to $A$). Then a reflection across line $\ell$ maps figure $D$ onto figure $E$.
## Step3: Analyze Option C
A reflection across line $\ell$ flips figure $E$. Then a translation along $\overrightarrow{AB}$ (left - ward)  would not map it onto figure $D$.
## Step4: Analyze Option D
A reflection across line $\ell$ flips figure $E$. Then a translation along $\overrightarrow{BA}$ (right - ward) maps figure $E$ onto figure $D$.
## Step5: Analyze Option E
A reflection across line $\ell$ flips figure $D$. Then a translation along $\overrightarrow{BA}$ (right - ward) would not map figure $D$ onto figure $E$.

# Answer:
B. A translation along $\overrightarrow{BA}$ followed by a reflection across line $\ell$ maps figure $D$ onto figure $E$.
D. A reflection across line $\ell$ followed by a translation along $\overrightarrow{BA}$ maps figure $E$ onto figure $D$.

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Question

Explanation:

Step1: Analyze Option A

Step2: Analyze Option B

Step3: Analyze Option C

Step4: Analyze Option D

Step5: Analyze Option E

Answer: