SOLUTION: Given that the four points A(1,2), B(2,-5), C(7,0) and D(p,q) are the vertices of rhombus ABCD. Calculate the value of p and q. Calculate the area of the rhombus.

Question 1178013: Given that the four points A(1,2), B(2,-5), C(7,0) and D(p,q) are the vertices of rhombus ABCD. Calculate the value of p and q. Calculate the area of the rhombus.
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
Let the vertices of a rhombus are A(1,2), B(2,-5), C(7,0) and D(p,q)
.
We know that diagonals of rhombus bisect each other,
∴ Co-ordinates of mid-points of AC= Co-ordinates of mid-points of BD

mid point of AC = (1+7)/2 , (2+0)/2
(4,1)
Mid point of BD = (p+2)/2 ,(q-5)/2

4=(p+2)/2
p+2=8
p=6
(q-5)/2=1
q=7
D~ (6,7)

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