SOLUTION: Quadrilateral KLMN has vertices K(2,3), L(7,3), M(4,7), and N (-1,7). Prove by means of coordinate geometry that KLMN is a rhombus.

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Question 1173692: Quadrilateral KLMN has vertices K(2,3), L(7,3), M(4,7), and N (-1,7). Prove by means of coordinate geometry that KLMN is a rhombus.
Answer by ikleyn(52787)   (Show Source): You can put this solution on YOUR website!
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Quadrilateral KLMN has vertices K(2,3), L(7,3), M(4,7), and N (-1,7). Prove by means of coordinate geometry that KLMN is a rhombus.
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Looking at the coordinates of points, you may see that 


    - the segment KL is horizontal  (y= 3)  having the length of 7-2 = 5;

    - the segment MN is horizontal  (y= 7)  having the length of 4-(-1) = 5.


It is just enough to conclude that the quadrilateral KLMN is a parallelogram.


Next, the length of the segment  KN is   =  = 5  and is equal to that of segment KL.


It is just enough to conclude that the parallelogram KLMN  is a rhombus.

Solved.



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