6. Coordinate Geometry
2
Unit 6.2 :
Division of a Line Segment
6.2.1 To find the mid-point of Two Given Points.
Formula
:
Midpoint M
=
+
+
2
,
2
2
1
2
1
y
y
x
x
Eg.
P(3, 2)
and
Q(5, 7)
Midpoint,
M =
+
+
2
7
2
,
2
5
3
=
(4 ,
2
9
)
E1
P(-4, 6) and Q(8, 0)
(2, 3)
E2
P(6, 3) and Q(2, -1)
(4, 1)
E3
P(0,-1), and Q(-1, -5)
(- ½ , -3)
6.2.2 Division of a Line Segment
Q divides the line segment PR in the ratio
PQ :
QR
=
m : n.
P(
x
,
y
), R(
x
,
y
)
Q
(x,y)
=
+
+
+
+
n
m
my
ny
n
m
mx
nx
2
1
2
1
,
(NOTE :
Students are strongly advised to sketch a line segment before applying the formula)
Eg1. The point P internally divides the line segment
joining the point M(3,7) and N(6,2) in the ratio 2 : 1.
Find the coordinates of point P.
P =
+
+
+
+
1
2
)
2
(
2
)
7
(
1
,
1
2
)
6
(
2
)
3
(
1
=
3
11
,
3
15
=
11
5,
3
E1. The point P internally divides the line segment
joining the point M (4,5) and N(-8,-5) in the ratio
1 : 3. Find the coordinates of point P.
5
1,
2
n
m
P(x
1
, y
1
)
R(x
2
, y
2
)
Q(x, y)
●
n
m
R(x
2
, y
2
)
P(x
1
, y
1
)
Q(x, y)
●
1
2
N(6,
2)
M(3, 7)
P(x, y)