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Question
The line segment joining the points M(5, 7) and N(–3, 2) is intersected by the y-axis at point L. Write down the abscissa of L. Hence, find the ratio in which L divides MN. Also, find the co-ordinates of L.
Solution
Since, point L lies on y-axis, its abscissa is 0.
Let the co-ordinates of point L be (0, y).
Let L divides MN in the ratio k : 1.
Using section formula, we have:
`x = (k xx (-3) + 1 xx 5)/(k + 1)`
`0 = (-3k + 5)/(k + 1)`
`-3k + 5 = 0`
`k = 5/3`
Thus, the required ratio is 5 : 3.
Now, `y = (k xx 2 + 1 xx 7)/(k + 1)`
= `(5/3 xx 2 + 7)/(5/3 + 1)`
= `(10 + 21)/(5 + 3)`
= `31/8`
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Activity:
∴ By section formula,
∴ x = `("m"x_2 + "n"x_1)/square`,
∴ x = `(3 xx 8 + 1 xx 4)/(3 + 1)`,
= `(square + 4)/4`,
∴ x = `square`,
∴ y = `square/("m" + "n")`
∴ y = `(3 xx 5 + 1 xx (-3))/(3 + 1)`
= `(square - 3)/4`
∴ y = `square`
