F.3 Mathematics Supplementary Notes
Chapter 9 Coordinate Geometry of Straight Lines
Chapter 9 Coordinate Geometry of Straight Lines
Important Terms
angle of inclination
gradient
line segment
perpendicular bisector
point of division
5/2006
Name:____________(
P. 1
) Class: F.3 ( )
point of intersection
slope
vertex (vertices)
Revision Notes
1. Distance between two points A(x1, y1) and B(x2 , y2) is :
AB  ( x1  x 2 ) 2  ( y1  y 2 ) 2
y
L
B(x2 , y2)
2.
y  y1
Slope(or gradient) of a straight line  2
x 2  x1

O
x
A(x1 , y1)
= tan 
where  is called the angle of inclination.
Note : The slope is positive for 0    90 and is negative for 90    180 .
3.
Point of division
Let A(x1 , y1) and B(x2 , y2) be two points . If P(x , y) divides
the line segment AB in the ratio m：n , then
x
mx2  nx1
mn
y
my2  ny1
mn
In particular, if P is the mid-point of AB , then
x  x2
x 1
2
4.
y  y2
y 1
2
Parallel and perpendicular lines
If two lines L1 and L2 are parallel, then
Slope of L1 = slope of L2
If two lines L1 and L2 are perpendicular, then
Slope of L1  slope of L2 = –1
B(x2 , y2)
AP : PB = m : n
P(x , y)
A(x1，y1)
F.3 Mathematics Supplementary Notes
Chapter 9 Coordinate Geometry of Straight Lines
5/2006
P. 2
Exercise:
1. Find the unknown in each of the following.
(a) A(1, 1), B(x, 4); slope of AB = 3.
(b) C(2a, –1), D(–a, 3); slope of CD= 
4
.
3
(c) G(–2, –3), H(2, n); inclination of GH = 45 .
2.
Given two points A(–6, 4) and B(4, –1). Find the ratio in which AB is divided by
(a) the point P(0, 1)
(b) the point Q(–2, 2)
3.
P is a point on a line segment AB such that AP：PB = 3：1. If the x-coordinates of A, B and P are
–2, 6 and k respectively, find the value of k.
4.
If the points (1, 1), (3, 2) and (7, k) are on the same straight line, find the value of k.
F.3 Mathematics Supplementary Notes
5
Chapter 9 Coordinate Geometry of Straight Lines
A(–1 , 4) and B(5 , –2) are two given points.
5/2006
P. 3
If AB cuts the y-axis at P, find the
coordinates of P.
y
A(–1,4)
P
x
O
B(5,–2)
6.
In the figure, ABCD is a parallelogram. Find the coordinates of D.
y
D
x
O
A(–1,–1)
C(2,–1)
B(–3,–4)
7.
In the figure, O is the origin and A is the point (8 , 2).
(a) B is a point on the x-axis such that the slope of AB is 1. Find the coordinates of B.
y
D
A(8,2)
O
(b) C is another point on the x-axis such that AB = AC. Find the coordinates of C.
B
C
x
F.3 Mathematics Supplementary Notes
Chapter 9 Coordinate Geometry of Straight Lines
5/2006
P. 4
M.C.Questions
1.
The distance between the points (a , b) and
(2a , –2b) is
A.
a 2  3b 2
B.
a 2  9b 2
D.
C.
a 2  9b 2
E.
5.
A.
B.
C.
3a 2  b 2
9a 2  b 2
6.
2.
P(7, 3) , Q(–1, 5) and R(–5, –2) are the
vertices of PQR. If S is the mid-point of PQ,
then RS =
A.
B.
C.
3.
4
8
10
D.
E.
6
12
In the figure, ABC is an isosceles triangle
with AB=AC. If B =(0 , –2) and C=(4 , 0),
find the coordinates of A.
7.
(0 , 3)
(0 , 4)
(0 , 5)
(4 , 0)
(5 , 0)
C(4,0)
O
A.
27o
B
C.
D.
E.
37o.
53o
72o
81o
(2, 5)
(–1, 1)

x
O
If the points A(–2 , 3), B(–3 , 5) and C(k , 7)
–4
–5
–6
D.
E.
–7
–8
x
A is a point on the x-axis. If the distance
between A and B(5 , 3) is 5, find the
coordinates of A .
(0 , 3) only
(1 , 0) only
(5 , 0) only
In the figure, find  , correct your answer to
the nearest degree.
y
A.
B.
C.
CE87Q29
8.
A.
B.
C.
D. (8, – 2)
E. (9, – 1)
A
B(0,–2)
4.
(5, – 5)
(6, – 4)
(7, – 3)
lie on a straight line, find the value of k.
y
A.
B.
C.
D.
E.
M(–1, –1) is the mid-point of the line
segment joining point A(– 8, 2) and point B.
Find the coordinates of B.
D.
E.
(1 , 0) or (9 , 0)
(3 , 0) or (5 , 0)
In the figure, the slopes of the lines L1 , L2 , L3
and L4 are m1 , m2 , m3 and m4 respectively.
Which of the following is true ?
y
L3
A. m1 > m2 > m3 > m4
B. m2 > m1 > m3 > m4
C. m1 > m2 > m4 > m3
D. m2 > m1 > m4 > m3
E. m4 > m3 > m2 > m1
L4
L2
L1
x
O
F.3 Mathematics Supplementary Notes
Chapter 9 Coordinate Geometry of Straight Lines
5/2006
P. 5
CE91Q28
9.
PQRS is a parallelogram with vertices
P =(0 , 0). Q = (a , b)and S = (–b , a). Find R.
A.
B.
C.
(– a , – b)
(a , – b)
(a – b, a – b)
D.
E.
(a – b, a + b)
(a + b , a + b)
CE92Q31
10. The mid-points of the sides of a triangle are
(3 , 4) , (2 , 0) and (4 , 2). Which of the
following points is a vertex of the triangle?
A.
B.
C.
(3.5 , 3)
(3 , 2)
(3, 1)
96CEQ53
13. A(–3 , 2) and B(1 , 3) are two points. C is a
point on the AB produced such that
AB：BC = 1：2. Find the coordinates of C.
A.
5 7
( , )
3 3
B.
1 8
( , )
3 3
C.
(3 ,
D. (5 , 4)
7
)
2
E. (9 , 5)
CE98Q33
D. (1.5, 2)
E. (1, 2)
14. In the figure, PQRS is a parallelogram. Find
the slope of PR.
y
CE94Q26
11. The points A(4 , –1) , B(2 , 3) and C(x , 5) lie
on a straight line. Find x.
A.
B.
C.
–5
–4
1
D.
E.
2
5
CE94Q27
12. In the figure, the shaded part is bounded by
the axes, the lines x = 3 and x + y =5. Find its
area.
y
x=3
A.
B.
C.
D.
E.
10.5
12
15
19.5
21
A.
13
15
B.
15
13
C.
9
11
D.
11
9
E.
5
x
S(–6, 7)
x
O
Q(5, –2)
P(–8, –4)
CE99Q31
15. A(–4, 2) and B(1,–3) are two points. C is a
point on the y-axis such that AC = CB. Find
the coordinates of C.
3
1
,  )
2
2
A.
(
B.
C.
D.
E.
(–1 , 0)
(1 , 0)
(0 , –1)
(0 , 1)
x +y =5
O
R
F.3 Mathematics Supplementary Notes
Chapter 9 Coordinate Geometry of Straight Lines
5/2006
P. 6
Ans: CCADBCADDECAEAB
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F.3 Mathematics Supplementary Notes
Chapter 9 Coordinate Geometry of Straight Lines
5/2006
P. 7