Quadrilaterals $A B C D$ and $K L M N$ are congruent.

Which of the following sequences of transformations maps $K L M N$ onto $A B C D$ ?
\begin{tabular}{ll}
Sequence A & Sequence B \
\hline A translation along the directed line segment & A reflection over the vertical line through \
$\overline{M A}$, then a reflection over the horizontal & point $N$, then a translation along the \
line through point $A$. & directed line segment $\overline{N B}$.
\end{tabular}

Choose 1 answer:
(A) Only sequence A
(B) Only sequence B
(c) Both
(D) Neither

Question

Quadrilaterals $A B C D$ and $K L M N$ are congruent.

Which of the following sequences of transformations maps $K L M N$ onto $A B C D$ ?
\begin{tabular}{ll} 
Sequence A & Sequence B \
\hline A translation along the directed line segment & A reflection over the vertical line through \
$\overline{M A}$, then a reflection over the horizontal & point $N$, then a translation along the \
line through point $A$. & directed line segment $\overline{N B}$.
\end{tabular}

Choose 1 answer:
(A) Only sequence A
(B) Only sequence B
(c) Both
(D) Neither

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ Analyze the given information about the positions of quadrilaterals $ABCD$ and $KLMN$. ‖ ‖ step 2 ⋮ Determine the vector for the translation by comparing the coordinates of corresponding points from $KLMN$ to $ABCD$. ‖ ‖ step 3 ⋮ Check if the translation vector from step 2 matches the directed line segment $\overline{MA}$ for Sequence A or $\overline{NB}$ for Sequence B. ‖ ‖ step 4 ⋮ Analyze the orientation of the two quadrilaterals to determine if a reflection is necessary and if so, over which line it should be. ‖ ‖ step 5 ⋮ Apply the transformations of Sequence A and Sequence B to see if either, both, or neither sequence maps $KLMN$ onto $ABCD$. ‖ ***C*** ∻Key Concept∻ ⚹Transformation Sequence⚹ ∻Explanation∻ ⚹To determine the correct sequence of transformations, one must analyze the translation vectors and the orientation of the figures to see if a reflection is required.⚹◊What formula can be used to calculate the distance between points on a coordinate plane?⍭ Generate me a similar question◊

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