Determine the ratio in which the line 2x + y –4 = 0 divides the line segment joining the points A (2,–2) and B (3, 7)
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Answer:
Step-by-step explanation:
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 ratio be k:1
Substituting (x
1
,y
1
)=(2,−2) and (x
2
,y
2
)=(3,7) in the
section formula, we get (
k+1
k(3)+1(2)
,
k+1
k(7)+1(−2)
)=(
k+1
3k+2
,
k+1
7k−2
)
Since 2x+y−4=0 divides the line at P, this point will lie on the
2(
k+1
3k+2
)+
k+1
7k−2
−4=0
6k+4+7k−2−4k−4=0
9k=2
k=
9
2
Hence, the ratio is 2:9
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