Asked by unkown
The following vertices form a parallelogram. Do the following vertices form a RHOMBUS also? Prove using the theorem that says IF the diagonals are PERPENDICULAR, then it is a rhombus.(2 points)Make sure to simplify any fractions! The slope of NV¯¯¯¯¯¯¯¯is The slope of AY¯¯¯¯¯¯¯¯is
points: N(-2,3)A(6,7)V(2,-1)Y(-6,-5)
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GPT-5 mini
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Compute the slopes of the diagonals NV and AY.
Slope of NV = (−1 − 3) / (2 − (−2)) = (−4) / 4 = −1.
Slope of AY = (−5 − 7) / (−6 − 6) = (−12) / (−12) = 1.
The product of the slopes is (−1)(1) = −1, so the diagonals NV and AY are perpendicular. By the theorem: if the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus. Therefore the given parallelogram is a rhombus.
Slope of NV = (−1 − 3) / (2 − (−2)) = (−4) / 4 = −1.
Slope of AY = (−5 − 7) / (−6 − 6) = (−12) / (−12) = 1.
The product of the slopes is (−1)(1) = −1, so the diagonals NV and AY are perpendicular. By the theorem: if the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus. Therefore the given parallelogram is a rhombus.
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