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The position vectors of points A and B with respect to the origin O are `((−8),(5 ))` and `((12),(−5))` 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 terms of OB
(c) Point P maps onto P’ by a translation `((−5),(8))`. Given that OP=OM+2MN, find the coordinates of P’.