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Answer: The correct option is a.Quadrilateral DEFG is a rhombus because opposite sides are parallel and all four sides have the same length.
Explanation:
It is given that coordinates of the vertices of quadrilateral DEFG are D(−2, 5) , E(2, 4) , F(0, 0) , and G(−4, 1) .
The distance formula for two points is given below,
Slope formula,
Slope of DE,
Slope of EF,
Slope of FG,
Slope of DG,
The slope of opposite sides are equal, it means the opposite sides are parallel.
All four sides do not have the same length. It means it is not a rhombus.
From the figure it is noticed that the opposite sides are parallel.
Therefore, the correct option is a.Quadrilateral DEFG is a rhombus because opposite sides are parallel and all four sides have the same length.
