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(52786)   (Show Source):
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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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