F4 Maths

1. P(0,2) and Q(2,1) divide the line segment AB in the ratio 1:2 and 2:1 respectively. Find the coordinates of A and B.

Let A = (p, q) and B = (r, s)

P(0,2) and Q(2,1) divide the line segment AB in the ratio 1:2 and 2:1 respectively:
[p + (1/2)r] / [1 + (1/2)] = 0 …… (1)
(p + 2r) / (1 + 2) = 2 …… (2)
[q + (1/2)s] / [1 + (1/2)] = 2 …… (3)
(q + 2s) / (1 + 2) = 1 …… (4)

(1):
p + (1/2)r = 0
r = -2p …… (5)

Put (5) into (2):
[p + 2(-2p)] / 3 = 2
p - 4p = 6
p = -2

Put p = -2 into (5):
r = -2 x (-2)
r = 4

(3):
(2q + s) / (2 + 1) = 2
2q + s = 6 …… (6)

(4):
q + 2s = 3 …… (7)

(6)x2 - (7):
3q = 9
q = 3

(7)x2 - (6):
3s = 0
s = 0
Put (6) into (3):

Hence, A = (-2, 3) and B = (4, 0)


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2. Find the slope (m) and angle of inclination (B) of the line jointing the following points. (Give B to the neaest minute)
P(3,0), Q(7,-6)

slope, m
= (0 + 6)/(3 - 7)
= -3/2

tanB = m
tanB = (-3/2)
Inclination B = 123°41' (to the nearest minute)