Question

The position vectors A and B with respect to the origin O,(-8,5) are (12,-5)and respectively. Point M is the midpoint of AB 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 term OB.
(c) Point P maps onto P' by a translation(-5,8). Give that OP = OM + 2MN, find the coordinates of
P'.