Question

Math

Posted 6 months ago

```
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
```

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Answer from Sia

Posted 6 months ago

Solution by Steps

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.

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