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Shtirlitz [24]
2 years ago
5

Decide whether quadrilateral ABCD with vertices 4(3,1), B(-1,-1) C(1,3), and D(5.5) is a rectangle, rhombus,square, or parallelo

gram.

Mathematics
1 answer:
Sergeeva-Olga [200]2 years ago
5 0

Answer: rhombus

Step-by-step explanation:

By inspection, we can tell that there are no right angles, so we can determine it is not a square or a rectangle.

From the options, it is implied that it is a parallelogram, so to determine if it is a rhombus, we can determine if there is a pair of consecutive congruent sides.

By the distance formula,

AB=\sqrt{(-1-3)^{2}+(-1-1)^{2}}=\sqrt{16+4}=2\sqrt{5}\\BC=\sqrt{(-1-1)^{2}+(-1-3)^{2}}=\sqrt{4+16}=2\sqrt{5}

As AB=BC, there is indeed a pair of consecutive congruent sides, and thus the most specific classification is a <em>rhombus</em>

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