The position vectors of points A and B with respect to the origin 0, are (-8,5) and (12,-5) respectively.

Question

Point M is the midpoint of B 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’.

Answer 1

A(-8,5), N(x1,y1), O(0,0), M(x2,y2), B(12,-5).

a. Point N:
x1-(-8) = 0-x1.
2x1 = -8.
x1 = -4.

y1-5 = 0-y.
2y1 = 5.
Y1 = 2.5.

Point M:
x2-0 = 12-x2.
2x2 = 12.
X2 = 6.

y2-0 = -5-y2.
2y2 = -5
Y2 = -2.5

(NM)^2 = (x2-x1)^2 + (y2-y1)^2 =
(6-(-4))^2 + (-2.5-2.5)^2 = 100 + 25 =
125.
NM = 11.18.

b. (OB)^2 = (X2)^2 + (Y2)^2 = 36 + 6.25 = 42.25.
OB = 6.5.

NM/OB = 11.18/6.5.
NM = 1.72*OB.

Answer 2

Where does the 1 on N come from?