Find the possible pairs of coordinates of the fourth vertex D of the parallelogram,if three of its vertices are A(5,6), B(1,-2)and C(3,-2).

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).