find the ratio in which the y axis divides the line segment joining the points (5,-6) and (-1,-4). Also find the point of intersec

2 thoughts on “find the ratio in which the y axis divides the line segment joining the points (5,-6) and (-1,-4). Also find the point of intersec”

1. Let the line segment A(5, -6) and B(-1, -4) is divided at point P(0, y) by y-axis in ratio m:n

   :. x = [tex]\frac{mx2+nx1}{m+n}[/tex] and y = [tex]\frac{my2+ny1}{m+n}[/tex]

   Here, (x, y) = (0, y); (x1, y1) = (5, -6) and (x2, y2) = (-1, -4)

   So , 0 = [tex]\frac{m(-1)+n(5)}{m+n}[/tex]

   => 0 = -m + 5n

   => m= 5n

   => [tex]\frac{m}{n}[/tex] = [tex]\frac{5}{1}[/tex]

   => m:n = 5:1

   Hence, the ratio is 5:1 and the division is internal.Now,

   y = [tex]\frac{my2+ny1}{m+n}[/tex]

   => y = [tex]\frac{5(-4)+1(-6)}{5+1}[/tex]

   => y = [tex]\frac{-20-6}{6}[/tex]

   => y = [tex]\frac{-26}{6}[/tex]

   => y = [tex]\frac{-13}{3}[/tex]

   Hence, the coordinates of the point of division is (0, -13/3).

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2. x1=5;y1=-6

   x2=-1;y2=-4

   Therefore,

   mx2+nx1/m+n

   0=m(-1)+n(5)/m+n

   0=-1m+5n/m+n

   -1m+5n=0

   m/n=5/1

   5:1

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