The position vectors of points A and B with respect to the origin 0, are (-8,5) and (12,-5) respectively.

Question

Point M is the midpoint of B and N is the midpoint of OA.

(a) Find:

(i) The coordinates of N and M

(ii) The magnitude of NM

(b) Express vector NM in terms of OB

(c) Point P maps onto P’ by a translation (-5,8) . Given that

OP = OM + 2MN, find the coordinates of p’.