Prove that the points (4,5),(7,6)!(6,3),(3,2) are the vertices of parallelogram.Is it a rectangle?
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Answer:
By distance formula we have,
Distance between two points =√ (x2−x1)²+(y2−y1)²
AB=√(7−4)²+(6−5)²
=√9+1
=√10
BC= √(6−7)²+(3−6)²
=√1+9
=√10
CD= √(3−6)²+(2−3)²
= √9+1
= √10
AD=(3−4)²+(2−5)²
= √1+9
= √10
∴ AB=CD and BC=AD
∴ Opposite sides are equal
Hence,ABCD is a parallelogram (Proved)
Also,AB=BC=CD=AD=10
i.e. all the sides are
equal.
Therefore,it is not a rectangle.
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