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Question

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


1785556_40259469a67340e18768908ea9c32473.PNG

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Solution

Using the section formula, if a point (x,y) divides the line joining the points (x1,y1) and (x2,y2) in the ratio m:n, then
(x,y)=(mx2+nx1m+n,my2+ny1m+n)

Let the point on y -axis be P(0,y) and
AP:PB=k:1

Therefore, using section formula:
5×1+(1)×kk+1=05k=0k=5
Hence, required ratio is 5:1.

Now,
y=(4)×5+(1)×65+1
=2066
=133
Hence, point on y -axis is P(0,133)

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