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Question
Find the ratio which the line segment joining the pints A(3, -3) and B(-2,7) is divided by x -axis Also, find the point of division.
Solution
The line segment joining the points A(3, -3) and B(-2,7) is divided by x-axis. Let the required ratio be k : 1 So ,
` 0= (k (7) -3)/(k+1) ⇒ k =3/7`
Now,
`"Point of division" = ((k(-2)+3)/(k+1 \) , (k(7)-3)/(k+1))`
`=((3/7 xx(-2)+3)/(3/7+1) , (3/7xx (7) -3)/(3/7 +1)) (∵ k = 3/7)`
`= ((-6+21)/(3+7), (21-21)/(3+7))`
`=(3/2,0)`
`"Hence, the required ratio is 3:7and the point of division is"(3/2, 0)`
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