Question

In what ratio the line segment joining the points (-2,-3) and (3,7) is divided by the y – axis ? Also, find the co – ordinates of the point of division

Answer 1

P(0,2) is the point of division

Answer 2

Answer:

Let the required point be P( 0, y)    

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)