7 The coordinates of two points \(A\) and \(B\) are \(( 1,3 )\) and \(( 9 , - 1 )\) respectively and \(D\) is the mid-point of \(A B\). A point \(C\) has coordinates \(( x , y )\), where \(x\) and \(y\) are variables.
- State the coordinates of \(D\).
- It is given that \(C D ^ { 2 } = 20\). Write down an equation relating \(x\) and \(y\).
- It is given that \(A C\) and \(B C\) are equal in length. Find an equation relating \(x\) and \(y\) and show that it can be simplified to \(y = 2 x - 9\).
- Using the results from parts (ii) and (iii), and showing all necessary working, find the possible coordinates of \(C\).