Question

Math

Posted 2 months ago

```
Quadrilateral $A B C D$ has the following vertices:
- $A(6,8)$
- $B(6,-5)$
- $C(-5,-10)$
- $D(-5,3)$
Is quadrilateral $A B C D$ a rhombus, and why?
Choose 1 answer:
(A) Yes, because $A B=B C=C D=A D$.
(B) Yes, because $\overline{A B} \| \overline{C D}$, and $\overline{B C} \| \overline{A D}$.
(C) No, because $\overline{A B}$ is longer than $\overline{B C}$.
(D) No, because $\overline{A B}$ is not parallel to $\overline{B C}$.
```

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Answer from Sia

Posted 2 months ago

Solution by Steps

step 2

Using the asksia-ll calculator results, we find that $AB = 13$, $BC = \sqrt{146} \approx 12.083$, $CD = 13$, and $AD = \sqrt{146} \approx 12.083$

step 3

Since $AB = CD$ and $BC = AD$, but $AB \neq BC$, the sides are not all equal

step 4

The asksia-ll calculator also confirms that lines $AB$ and $CD$ are parallel, as well as lines $BC$ and $AD$

step 5

However, for a quadrilateral to be a rhombus, all four sides must be equal in length, which is not the case here

1 Answer

D

Key Concept

Properties of a Rhombus

Explanation

A rhombus is a quadrilateral with all sides equal in length. While $ABCD$ has opposite sides that are parallel, $AB$ and $BC$ are not equal, thus $ABCD$ is not a rhombus.

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