Question

Prove that the points (4,5),(7,6),(4,3) and (1,2) are vertices of the parallelogram

Answer 1

Step-by-step explanation:

let the vertices of a parallelogram be A(4,5),B(7,6),C(6,3)D(3,2)

So 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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