Maths

164 MATHEMATICS
Example 6 : Find the coordinates of the point which divides the line segment joining
the points (4, – 3) and (8, 5) in the ratio 3 : 1 internally.
Solution : Let P(x, y) be the required point. Using the section formula, we get
Therefore, (7, 3) is the required point.
x = 3(8) 1(4) ✁ 7 , y = 3(5) 1(–3) 3 ✁
3 1
3 1
Example 7 : In what ratio does the point (– 4, 6) divide the line segment joining the
points A(– 6, 10) and B(3, – 8)?
Solution : Let (– 4, 6) divide AB internally in the ratio m 1
: m 2
. Using the section
formula, we get
3m1 6 m2 –8 ✂
✄
1
☎
10 ✆
2
(– 4, 6) =
,
m m
✞
✝
✠
✟
✆
✆ m m m m
1 2 1 2
Recall that if (x, y) = (a, b) then x = a and y = b.
(1)
So, – 4 =
3m
6 ✡ m
m m
1 2
1 2
and
6
✁
8m
10 ✡ m
m m
1 2
1 2
Now, – 4 =
3m
6 ☛ m
☞ m m
1 2
1 2
gives us
– 4m 1
– 4m 2
=3m 1
– 6m 2
i.e., 7m 1
=2m 2
i.e., m 1
: m 2
=2 : 7
You should verify that the ratio satisfies the y-coordinate also.
Now,
8m
10 ✡ m
m m
1 2
1 2
=
m
✌ ✍
m2
m
✍
1
1
m
1
8 10
2
(Dividing throughout by m 2
)
=
2
8 10
✎ ✑ ✏
7
✒ 6
2
✑ 1
7