"Use analytic geometry to classify the quadrilateral with..." solved and explained

Baublysiz

Answered question

2021-11-22

Use analytic geometry to classify the quadrilateral with vertices J(-2,1), K(2, 3), L(4, -1), and N(0.-3). Explain your reasoning and show all your work

Answer & Explanation

Mollicchiuk

Beginner2021-11-23Added 13 answers

JKLM is a quadrilateral with verdives

J(-2,1), K(2,3), L(4,-1) and N(0,-3)

\overset{―}{J K} = \sqrt{{(3 - 1)}^{2} + {(2 + 2)}^{2}} = \sqrt{4 + 16} = \sqrt{20}

L N = \sqrt{{(- 3 + 1)}^{2} + {(0 - 4)}^{2}} = \sqrt{4 + 16} = \sqrt{20}

K L = \sqrt{{(- 1 + 3)}^{2} + {(4 - 0)}^{2}} = \sqrt{4 + 16} = \sqrt{20}

N J = \sqrt{{(1 + 3)}^{2} + {(- 2 - 0)}^{2}} = \sqrt{4 + 16} = \sqrt{20}

N K = \sqrt{{(3 + 3)}^{2} + {(2 - 0)}^{2}} = \sqrt{36 + 4} = \sqrt{40}

J L = \sqrt{{(- 1 - 1)}^{2} + {(4 + 2)}^{2}} = \sqrt{4 + 36} = \sqrt{40}

Here

J K = N L

K L = J N

and

N K = J L

opposite sides are equal and diagonal are equal
Hence LKLN is a rectangle.

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