Write the co-ordinates of E such that the parallelogram ABCE is a rhombus. I'm unsure how to do this and it's always in my exams. (The original shape was a triangle and E was originally not a point) 
A:(1,0) B:(0,8) C(7,4)
Gradient of AC:2/3
AC equation:2x - 3y - 2 = 0 
Coordinates of the midpoint D of AC: 4,2


*

*AC is perpendicular to BD

*ABC is an isosceles
Area of triangle = 26 u

The diagonals of a rhombus bisect each other at right angles (Proof)
If $O(p,q)$  is the midpoint of $AC, B E$
If $E(h,k)$  $$\dfrac{1+7}2=p=\dfrac{0+h}2$$  and  $$\dfrac{0+4}2=q=\dfrac{8+k}2$$
