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Consider quadrilateral JKLM with vertices at [tex]\( (0, 0) \)[/tex], [tex]\( K(4, 0) \)[/tex], [tex]\( L(7, 4) \)[/tex], and [tex]\( M(3, 4) \)[/tex]. Which of these statements correctly describes how we can classify quadrilateral JKLM?

A. Quadrilateral JKLM can be identified as a parallelogram because both pairs of opposite sides are parallel.
B. Quadrilateral JKLM can be identified as a parallelogram because all four sides are congruent.
C. Quadrilateral JKLM can be identified as a rhombus because all four sides are congruent.
D. Quadrilateral JKLM can be identified as a rhombus because both pairs of opposite sides are parallel.



Answer :

GinnyAnswer
To classify quadrilateral JKLM with given vertices J(0, 0), K(4, 0), L(7, 4), and M(3, 4), let us follow a systematic step-by-step approach:

1. Identify pairs of opposite sides:
- JK and LM
- JM and LK

2. Calculate the slopes of each side:
- Slope of JK: (K[1] - J[1]) / (K[0] - J[0]) = (0 - 0) / (4 - 0) = 0
- Slope of LM: (M[1] - L[1]) / (M[0] - L[0]) = (4 - 4) / (3 - 7) = 0
- Slope of JM: (M[1] - J[1]) / (M[0] - J[0]) = (4 - 0) / (3 - 0) = 4/3
- Slope of LK: (K[1] - L[1]) / (K[0] - L[0]) = (0 - 4) / (4 - 7) = 4/3

- We notice that JK and LM are both horizontal lines (slopes of 0), meaning they are parallel.
- We also notice that JM and LK have the same slope (4/3), meaning they are parallel to each other as well.

3. Conclusion based on slopes:
- Both pairs of opposite sides (JK parallel to LM and JM parallel to LK) are parallel, so quadrilateral JKLM is a parallelogram.

Since we have determined that JKLM is a parallelogram based on the fact that both pairs of its opposite sides are parallel, the correct statement to describe and classify quadrilateral JKLM is:

Quadrilateral JKLM can be identified as a parallelogram because both pairs of opposite sides are parallel.

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