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On a coordinate plane, parallelogram K L M N shown. Point K is at (7, 7), point L is at (5, 3), point M is at (1, 1), and point N is at (3, 5).
Which statement proves that parallelogram KLMN is a rhombus?
The midpoint of both diagonals is (4, 4).
The length of KM is StartRoot 72 EndRoot and the length of NL is StartRoot 8 EndRoot.
The slopes of LM and KN are both One-half and NK = ML = StartRoot 20 EndRoot.
The slope of KM is 1 and the slope of NL is –1.
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"The slope of KM is 1 and the slope of NL is –1."
Reason: slope(KM) = (1−7)/(1−7) = 1 and slope(NL) = (3−5)/(5−3) = −1, so the diagonals KM and NL are perpendicular. In a parallelogram, perpendicular diagonals imply the figure is a rhombus, so KLMN is a rhombus.
Reason: slope(KM) = (1−7)/(1−7) = 1 and slope(NL) = (3−5)/(5−3) = −1, so the diagonals KM and NL are perpendicular. In a parallelogram, perpendicular diagonals imply the figure is a rhombus, so KLMN is a rhombus.
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