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Question

Show that the points A(1,0),B(5,3),C(2,7) and D(2,4) are the vertices of a parallelogram.

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Solution

We have, A(1,0),B(5,3),C(2,7) and D(2,4)

So by distance formula we have,

Distance between two points = (x2x1)2+(y2y1)2


AB=(51)2+(3)2=5BC=(52)2+(37)2=5CD=(22)2+(74)2=5DA=(1+2)2+(4)2=5

Opposite sides of a parallelogram are equal. Here, Also opposite sides are equal.
ABCD is a parallelogram. ( HENCE PROVED)

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