Question

find the ratio in which the point P(3/4,5/12) divides the line segment joining the points A(1/2,3/2) and B(2,-5) .

Answer 1

Hi ,

We know that the section formula
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The point which divide the line segment

joining the points A ( x1 , y1 ) , B ( x2 , y2 ) in the ratio k:1

is P ( kx2+ x1/k +1 , ky2 + y1 / k+ 1 )

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According to the given problem ,

A( x1 , y1 ) = ( 1/2 , 3 /2 )

B ( x2 , y2 ) = ( 2 , -5 )

P ( x , y ) = ( 3 / 4 , 5 / 12 )

Let the ratio = k : 1

x = 3/4 ( given

(kx2 + x1 ) / ( k+ 1 ) = x

( k× 2 + 1/2 ) / ( k + 1 ) = 3 / 4

2k + 1/2 = 3 /4 ( k + 1 )

4 ( 2k + 1 / 2) = 3 ( k + 1 )

8k + 2 = 3k + 3

8k - 3 k = 3 - 2

5k = 1

k = 1/5

Therefore ,

Required ratio = k : 1

= 1 /5 : 1

= 1 : 5

P divides the line segment joining the piints A and B

in the ratio 1 : 5

I hope this helps you.

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Answer 2

Let the ratio be k:1

By section formula,

(2k+1/2/k+1, -5k+3/2)=(3/4,5/12)

2k+1/2/k+1=3/4     (Taking one of them)

By cross multiplication,

8k+4/2=3k+3

8k+2=3k+3

8k-3k=3-2

5k=1

K=1/5

Therefore the ratio is 1:5

I hope it helps you

Thanks