Question
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.
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'.
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'.
Answers
Steve
(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)
(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)