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)?

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Answer 1 · 2016-03-13T08:39:45

It is a rhombus.

L:#(7,5)#, M:#(5,0)#, N:#(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)=sqrt29#

MN=#sqrt((3-5)^2+(5-0)^2)=sqrt(4+25)=sqrt29#

NP=#sqrt((5-3)^2+(10-5)^2)=sqrt(4+25)=sqrt29#

PL=#sqrt((5-7)^2+(10-5)^2)=sqrt(4+25)=sqrt29#

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