Question

In what ratio is the line segment joining the points (-2,-3) and (3,7) divided by the y axis . Also find the coordinates of points of division .

Answer 1

Let the required point be P( 0, y)    [B'coz the point lies on y-axis]
Also, let the required ratio be k : 1

Using section formula,
P(0,y) = [(m1*x2+m2*x1) / m1+m2 , (m1*y2 +m2*y1) / m1+ m2]

Substituting values m1=k , m2=1, x1= -2 ,x2= 3 ,  y1=-3, y2=7, We get
P(0.y) = [ (3*k +1*-2)/ k+1 , (7*k +1*-3) /k+1]

P(0,y) = [ (3k-2)/ k+1 , (7k-3)/ k+1]
0= (3k-2)/k+1...(a)  ,  y= (7k-3)/k+1......(b)

(a) ..3k-2 = 0 

3k = 2

k=2/3

Sub k= 2/3 in (b)

y = (7*(2/3) - 3)/ (2/3)+1

   =(14/3 - 3)/ 5/3

   = (14-9)/3 / (5/3)

   = (5/3) /(5/3)

   = 1

Therefore ratio is k :1 = 2/3 :1 = 2:3
and point of division is P( 0,1)

Answer 2

Let the ratio be K: 1
are[-2+3k/k+1,-3+7k/k+1]
since,the point lie on the y-axis,the x-coordinate is 0
.: -2+3k/k+1=0
.: -2+3k=0
.:k=2/3
.: the required ratio is 2:3
coordinates of the point =[-6+6/2+3,-9+14/5]
=(0,1)