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ICSE Class 10 Answered

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.
Asked by priyanshumarwaha | 23 Mar, 2022, 09:36: AM
answered-by-expert Expert Answer
Let L divides MN in the ratio k:1.
As L lies on y-axis, its abscissa is 0.
Let L be (0, a).
By section formula, we have
open parentheses 0 comma straight a close parentheses equals open parentheses fraction numerator straight k open parentheses negative 3 close parentheses plus 5 over denominator straight k plus 1 end fraction comma fraction numerator straight k left parenthesis 2 right parenthesis plus 7 over denominator straight k plus 1 end fraction close parentheses
rightwards double arrow fraction numerator negative 3 straight k plus 5 over denominator straight k plus 1 end fraction equals 0 space space and space space fraction numerator 2 straight k plus 7 over denominator straight k plus 1 end fraction equals straight a
rightwards double arrow negative 3 straight k plus 5 equals 0 space space and space space fraction numerator 2 straight k plus 7 over denominator straight k plus 1 end fraction equals straight a
rightwards double arrow straight k equals 5 over 3
rightwards double arrow straight a equals fraction numerator 2 cross times begin display style 5 over 3 end style plus 7 over denominator begin display style 5 over 3 end style plus 1 end fraction
rightwards double arrow straight a equals fraction numerator 10 plus 21 over denominator 5 plus 3 end fraction equals 31 over 8
Hence comma space straight L space is space open parentheses 0 comma 31 over 8 close parentheses space which space divides space MN space in space the space ratio space 5 colon 3.
Answered by Renu Varma | 29 Mar, 2022, 10:29: AM

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