(Q31) Find the coordinates of the point which divide the line segment joining the points (a+b,a-b) and (a-b,a+b) in the ratio 3:2 internally.
Answer
Given A(a+b,a-b) and B(a-b,a+b).
Let P(x,y) divides AB in the ratio 3:2 internally.
section formula=
(
m
1
x
2
+m
2
x
1
m
1
+m
2
,
m
1
y
2
+m
2
y
1
m
1
+m
2
)
= (
3(a-b)+2(a+b)
3+2
,
3(a+b)+2(a-b)
3+2
)
= (
3a-3b+2a+2b
5
,
3a+3b+2a-2b
5
)
= (
a-
b
5
,
a+
b
5
)
Clear