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 $\overline{B C}$.

Question

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 $\overline{B C}$.

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ To determine if quadrilateral $ABCD$ is a rhombus, we need to check if all sides are equal and if opposite sides are parallel. ‖ ‖ 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 $AB eq BC$, 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.⚹◊What is the formula to calculate the distance between two points on a plane given their coordinates?⍭ Generate me a similar question◊

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