Problem

Using the inclusive definition of a rhombus, verify that the ordered vertices \(J(-2,1)\), \(K(1,5)\), \(L(5,2)\), \(M(2,-2)\) form rhombus \(JKLM\). Give \(\text{all}~\text{four}~\text{squared}~\text{side}~\text{lengths}\), compare them, and state the conclusion.

Source coordinate plane: Quadrilateral JKLM has vertices J(-2,1), K(1,5), L(5,2), and M(2,-2); no side lengths or rhombus conclusion are shown.

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squared side lengths = JK²=25, KL²=25, LM²=16, MJ²=16; equality = not all four are equal; conclusion = JKLM is not a rhombus

squared side lengths = JK²=25, KL²=25, LM²=25, MJ²=25; equality = all four equal; conclusion = JKLM is not a rhombus because the values are squared lengths

squared side lengths = JK²=25, KL²=25, LM²=25, MJ²=25; equality = all four are equal and positive; conclusion = JKLM is a rhombus

squared side lengths = JK²=25, KL²=25, LM²=25, MJ²=7; equality = not all four are equal; conclusion = JKLM is not a rhombus

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Using the inclusive definition of a rhombus, verify that the ordered vertices \(J(-2,1)\), \(K(1,5)\), \(L(5,2)\), \(M(2,-2)\) form rhombus \(JKLM\). Give \(\text{all}~\text{four}~\text{squared}~\text{side}~\text{lengths}\), compare them, and state the conclusion.

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