Find the ratio in which (-8,3) divides the line segment joining the points (2,-2) and (-4,1).
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Answer:
Using the section formula, if a point (x,y) divides the line joining the points (x
1
,y
1
) and (x
2
,y
2
) in the ratio m:n, then (x,y)=(
m+n
mx
2
+nx
1
,
m+n
my
2
+ny
1
)
Substituting (x
1
,y
1
)=(3,4) and (x
2
,y
2
)=(−2,−1) in the section formula, we get the point (
m+n
m(−2)+n(3)
,
m+n
m(−1)+n(4)
)=(
m+n
−2m+3n
,
m+n
−m+4n
)
As the point lies on x - axis, y -coordinate =0.
=>
m+n
−m+4n
=0
=>m=4n or m:n=4:1
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