The position vectors 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.

Question

a) Find:
i) The coordinates of N and M;

Point N = OA

N = (0 + -8)/2, (0 +5)/2
= (-4, 2.5)
Point M = AB
M = (-8+12)/2, (5+ (-5)/2
= (2, 0)

ii) The magnitude of NM (3 marks)

NM = (6) (6) + (2.5) (2.5)
NM = 36 +6.25
= 42.25
= 6.5

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'.

Answer 1

(a) correct
(b) Since NM is not parallel to OB, it cannot be expressed in terms of OB alone. We do know that

ON + NM = (OB-OA)/2
OA/2 + NM = OB/2 - OA/2
NM = OB/2 - 3/2 OA

(c)
OP = OM + 2MN
= (2,0)+2(-6,2.5)
= (2,0)+(-12,5)
= (-10,5)
So, P' = (-15,13)