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Question

Determine the ratio in which the line 3x+y−9=0 divides the line segment joining the points (1,3) and (2,7).

A
4:3
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B
3:5
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C
3:7
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D
3:4
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Solution

The correct option is B 3:4

Using the section formula, if a point (x,y) lying on the given line divides the line joining the points (x1,y1) and (x2,y2) in the ratio m:n, then (x,y)=(mx2+nx1m+n,my2+ny1m+n)
Let the ratio be k:1

Substituting (x1,y1)=(1,3) and (x2,y2)=(2,7) in the section formula, we get,

P = (k(2)+1(1)k+1,k(7)+1(3)k+1)=(2k+1k+1,7k+3k+1)


Since P lies on the line 3x+y9=0, we have

3(2k+1k+1)+(7k+3k+1)9=0

6k+3+7k+39(k+1)=0

13k+69k9=0

4k3=0

k=34

Hence, the ratio is 3:4


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