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Is a shape a kite, parallelogram, or a rhombus if it has these coordinates: L: (7,5) M: (5,0) N: (3,5) P: (5,10)?

1 Answer

Shwetank Mauria

Mar 13, 2016

It is a rhombus.

Explanation:

L: $(7, 5)$ $(7,5)$ , M: $(5, 0)$ $(5,0)$ , N: $(3, 5) and P :$ $(3,5) and P:$ (5,10)#. Let us find length of LM, MN, NP and PL

LM= $\sqrt{{(5 - 7)}^{2} + {(0 - 5)}^{2}} = \sqrt{4 + 25} = \sqrt{29}$ $sqrt((5-7)^2+(0-5)^2)=sqrt(4+25)=sqrt29$

MN= $\sqrt{{(3 - 5)}^{2} + {(5 - 0)}^{2}} = \sqrt{4 + 25} = \sqrt{29}$ $sqrt((3-5)^2+(5-0)^2)=sqrt(4+25)=sqrt29$

NP= $\sqrt{{(5 - 3)}^{2} + {(10 - 5)}^{2}} = \sqrt{4 + 25} = \sqrt{29}$ $sqrt((5-3)^2+(10-5)^2)=sqrt(4+25)=sqrt29$

PL= $\sqrt{{(5 - 7)}^{2} + {(10 - 5)}^{2}} = \sqrt{4 + 25} = \sqrt{29}$ $sqrt((5-7)^2+(10-5)^2)=sqrt(4+25)=sqrt29$

As all the sides are equal, it is a rhombus.

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