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 $$\dfrac{0+4}2=q=\dfrac{8+k}2$$