Find the ratio in which the point P( 3, 4) divides the line segment joining A(1,2) and B(6,7).
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Answer:
Correct option is
B
1:5
We know that by section formula, the co-ordinates of the points which divide internally the line segment joining the points (x
1
,y
1
) and (x
2
,y
2
) in the ratio m:n is
P(x,y)=(
m+n
mx
2
+nx
1
,
m+n
my
2
+ny
1
)
Let point P divide AB in the ratio 1:k
Then, by section formula,
(
4
3
,
12
5
)≡
⎝
⎜
⎜
⎜
⎛
k+1
k(
2
1
)+1(2)
,
k+1
k(
2
3
)+1(−5)
⎠
⎟
⎟
⎟
⎞
Equating x and y coordinates, we get
k+1
k/2+2
=
4
3
,
k+1
3k/2−5
=
12
5
⇒2k+8=3k+3,18k−60=5k+5
⇒k=5
Hence P divides AB in the ratio 1:5
solution
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