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.

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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
$x equals fraction numerator k cross times left parenthesis negative 3 right parenthesis plus 1 cross times 5 over denominator k plus 1 end fraction 0 equals fraction numerator negative 3 k plus 5 over denominator k plus 1 end fraction minus 3 k plus 5 equals 0 k equals 5 over 3 T h u s space t h e space r e q u i r e d space r a t i o space i s space 5 colon 3 N o w comma y equals fraction numerator k cross times 2 plus 1 cross times 7 over denominator k plus 1 end fraction space equals fraction numerator begin display style 5 over 3 end style cross times 2 plus 7 over denominator begin display style 5 over 3 end style plus 1 end fraction space equals fraction numerator 10 plus 21 over denominator 5 plus 3 end fraction space equals 31 over 8$

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