A(1,2), B(3,-1), C(-1,-1). If ABCD is a parallelogram, find the coordinates of D.

Here are the solutions to the problems:

a) (i) Find the coordinates of D
Assuming ABCD is a parallelogram, the diagonals bisect each other. This means the midpoint of AC is the same as the midpoint of BD.
Given points: $A(1,2)$, $B(3,-1)$, $C(-1,-1)$. Let $D(x_D, y_D)$.

Step 1: Find the midpoint of AC.

$$M_{AC} = \left(\frac{x_A + x_C}{2}, \frac{y_A + y_C}{2}\right)$$ $$$$