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.

Question

(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'.

Answer 1

I will be happy to check your thinking on this,it seems straightforward to me.

Answer 2

A)
M= AB
= (-8+ 12)/2, (5 - (-5))/2
= (2, 0)
N = OA
(0 + -8)/2, (0 + 5)/2
= (-4, 2.5)
|NM| = 36 + 6.25
= 42.25
NM = 6.5

B) NM = OB
= (12 + 0)/2, (-5 + 0)/2
= (6, -2.5)
|NM| = 10(10) + (-5)(-5)
= 100 + 25
= 125
= 11.18
= 11.18/6.5
= 1.82

C)

Answer 3

A=(-8,5)
B=(12,-5)

M = (A+B)/2 = (2,0)
N = A/2 = (-4,5/2)
NM∥OB and NM=OB/2

OP=OM+2MN = OM-OB
OP' = OP+(-5,8)

Answer 4

I am still not get a solution C

Answer 5

(1, 0) - (6, -2.5)
= (-5, . 2.5)