The correct option is A 3:7
Given points are (−3,5) and (7,2)
Let the ratio be m:n
Now, the required coordinates of point on y− axis
=(7m−3nm+n,2m+5nm+n)
As the point lies on y− axis, so x coordinate will be zero, we get
7m−3nm+n=0
⇒7m−3n=0
∴mn=37
Alternate method:
If coordinates of two points are (x1,y1) and (x2,y2)
Let y− axis divides it in ratio of m:n,
The x− coordinate will be 0.
mx2+nx1m+n=0⇒mx2=−nx1⇒mn=−x1x2
Now, in our given question
x1=−3,x2=7∴mn=37