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A student draws parallelogram WXYZ on the coordinate plane. Then, the student translates the parallelogram 3 units up and 4 units to the right to form parallelogram PQRS.

Which statement must be true about parallelogram PQRS?

A. \( \overline{PQ} \) must be perpendicular to \( \overline{QR} \).

B. \( \overline{PQ} \) must be perpendicular to \( \overline{SR} \).

C. \( \overline{PQ} \) must be parallel to \( \overline{QR} \).

D. \( \overline{PQ} \) must be parallel to \( \overline{SR} \).

Answer :

Final answer:

When a parallelogram is translated, its sides maintain their length and parallel relationships. Therefore, the correct statement is that PQ must be parallel to QR.

Explanation:

When a parallelogram is translated, all its sides maintain their length and parallel relationships. The translation only changes the position of the parallelogram. In this case, the student translated parallelogram WXYZ 3 units up and 4 units to the right to form parallelogram PQRS. Therefore, PQ and QR, as well as PQ and SR, are still parallel to each other.

So, the correct statement would be:
PQ—— must be parallel to QR——.

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