4 It is given that \(A B C D\) is a quadrilateral. The position vector of \(A\) is \(\mathbf { i } + \mathbf { j }\), and the position vector of \(B\) is \(3 \mathbf { i } + 5 \mathbf { j }\).
- Find the length \(A B\).
- The position vector of \(C\) is \(p \mathbf { i } + p \mathbf { j }\) where \(p\) is a constant greater than 1 .
Given that the length \(A B\) is equal to the length \(B C\), determine the position vector of \(C\).
- The point \(M\) is the midpoint of \(A C\).
Given that \(\overrightarrow { M D } = 2 \overrightarrow { B M }\), determine the position vector of \(D\).
- State the name of the quadrilateral \(A B C D\), giving a reason for your answer.