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Question
In what ratio is the line segment joining the points A(-2, -3) and B(3,7) divided by the yaxis? Also, find the coordinates of the point of division.
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Solution
Let AB be divided by the x-axis in the ratio :1 k at the point P.
Then, by section formula the coordination of P are
`p = ((3k-2)/(k+1) , (7k-3)/(k+1))`
But P lies on the y-axis; so, its abscissa is 0.
Therefore , `(3k-2)/(k+1) = 0`
`⇒ 3k-2 = 0 ⇒3k=2 ⇒ k = 2/3 ⇒ k = 2/3 `
Therefore, the required ratio is `2/3:1`which is same as 2 : 3
Thus, the x-axis divides the line AB in the ratio 2 : 3 at the point P.
Applying `k= 2/3,` we get the coordinates of point.
`p (0,(7k-3)/(k+1))`
`= p(0, (7xx2/3-3)/(2/3+1))`
`= p(0, ((14-9)/3)/((2+3)/3))`
`= p (0,5/5)`
= p(0,1)
Hence, the point of intersection of AB and the x-axis is P (0,1).
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