in what ratio is the line segment-3,-1 and -8,-9 divided at the point-5,-25/5
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Step-by-step explanation:
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
)
Let the required ratio be k:1
Substituting (x
1
,y
1
)=(−3,−1) and (x
2
,y
2
)=(−8,−9) in the
section formula, we get (
k+1
k(−8)+1(−3)
,
k+1
k(−9)+1(−1)
)=(−5,−
5
21
)
(
k+1
−8k−3
,
k+1
−9k−1
)=(−5,−
5
21
)
Comparing the x - coordinate,
=>
k+1
−8k−3
=−5
=>−8k−3=−5k−5
3k=2
k=
3
2
Hence, the required ratio is 2:3.
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