Maths q 3 unit (1 Viewer)

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I would be so grateful if someone could please help me with just this one question!!! Its really bugging me
If you have the Cambridge 3 unit year 11 textbook it is q11 (g) of 5D! So on the number plane, points A (1,0) B (0,8) and C (7,4) form a triangle with D (4, 2) the midpoint of AC. Write down the coordinates of a point E such that ABCE is a rhombus. The answer is E(8,-4) - please help!!

 

[Drongoski]

Let co-ords of D be (a,b)

Then mid-point of BD = mid-point of AC

Taking x part and y part in turn:

(a+0)/2 = (1+7)/2 ==> a = 8

(b+8)/2 = (0+4)/2 ==> b = -4

 

[Coetez]

Yup pretty much as Drongoski said, since diagonals in a rhombus bisect each other, ED = BD and are concurrent then just go from there.

 

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That makes so much sense now! thank you so much guys