D is the midpoint of BC, so $D = \left(\dfrac{6+0}{2}, \dfrac{4+0}{2}\right) = (3, 2)$.
$$AD = \sqrt{(5-3)^2 + (-6-2)^2} = \sqrt{4 + 64} = \sqrt{68} \text{ units}$$
Answer: (a) $\sqrt{68}$ units
Source: Chapter 7, Section 7.2 (Distance Formula) and Section 7.3 (Mid-point Formula)
Since AD is a median, D is the midpoint of BC. Use the midpoint formula to find D, then apply the distance formula between A(5, −6) and D(3, 2). Students often forget to first find the midpoint — that is the key step examiners look for before applying the distance formula.