Page 292 - MATHEMATICS COURSE FOR SECONDARY SCHOOLS BOOK 2

These problems can also be solved using ratios and scalar multiplication of vectors.
(a)
EXERCISE 13.9
and x is the mid-point of OP,
(b)
32
(c)
OX : XQ = 1 : 5, find OX.
(d)
Since AY : YB = 4 : 5
-45
If EF = 36 and Y is a point on EF such that
Since OX : XP = 1:1 ThenOX =12O.P
1.
Given that OP = 10
So OX = Since AY : YB = 1:1
OX : XP = 2 : 5, find OX.
6 Then AY = 12 AB
Given that AB = 24 and y is a point on AB such that ()
AY : YB = 3: 5, find AX.
So AY=
Since OX : OP = 2: 3 Then OX= 25 OP
(25) 25 15
()
So OX = 10 ()
Then AY =
18 -12
= 2 12 2.
find AY.
Given that OP = 28 and x is a point on OP such that
(1 1
) 1 (-10)
=2x8
2 x 12 (4 )
3.
4.
5. 6. 7.
8.
9.
10.
11. 12.
14 ()
=2 -6 = 2 x[-10)
-12
(1 1
Let OQ = and x is the mid-point of OQ, find OX.
) = x[-6]
()
(2) -3
-10
Let MN = 8 and Y is the mid-point of MN, find MY.
-5
(2
2 x [-6]
and Y is a point on MN such that MY : YN = 2 : 3, find MY.
CX : XD = 3 : 4, calculate CX.
EY : YF = 2 : 7, evaluate EY.
6
49
4 9
9 (4
5
If CD = 35 and X is a point on CD such that -28
) AB
(-36) 27
5 x [-10]
x [-36]
and x is a point on GH such that GX : XH = 5 : 3, calculate GX.
49 x 27 4 x [-4]
()
() 4 x3
(-16) So OX = 12
If UV = 48 -96
)
-40
286
find OX.
Given that AB = -8 and Y is the mid-point of AB, () ()
-10 ()
() 16
Let OQ = 30 and X is a point on OQ such that -24
Let MN = 35 25
If GH = -24 ()
()
()
()
and Y is a point on UV such that UV : YV = 7 : 5, evaluate UY