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प्रश्न
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.
उत्तर
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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