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Question

The ratio in which y− axis divides the line segment joining (−3,5) and (7,2) is

A
3:7
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B
2:7
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C
3:8
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D
3:5
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Solution

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
=(7m3nm+n,2m+5nm+n)

As the point lies on y axis, so x coordinate will be zero, we get
7m3nm+n=0
7m3n=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=0mx2=nx1mn=x1x2
Now, in our given question
x1=3,x2=7mn=37

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