Q. 213.7( 20 Votes )

Find the possible

Answer :

According to the distance formula, the distance 'd' between two points (a,b) and (c,d) is given by
.....(1)


Slope of a line between two points (a,b) and (c,d) is



In the given question, for it to be a parallelogram AD = BC and slope AD = Slope BC


And


AB = DC and Slope AB = Slope CD


Let D be (x,y)


As AD = BC we get


= = 2 ....i


As AB = CD we get


= = 4 .....ii


As slope AD = Slope BC


....iii


As slope AB = Slope DC


.....iv


From iii we gey y = 6


Putting y = 6 in (i) we get


x = 3


and putting y = 6 in (ii) we get x = 7


Hence the possible coordinates of the point D are (7,6) and (3,6).


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