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Question

Point P divides the line segment joining the points A(1,3) and B(9,8) such that APPB=k1. If P lies on the line xy+2=0, find the value of k.

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Solution

We know that by section formula, the co-ordinates of the points which divide internally the line segment joining the points (x1,y1) and (x2,y2) in the ratio m:n are
(x,y)=(mx2+nx1m+n,my2+ny1m+n)

According to given conditions ,let's say coordinates of point P are (x,y)

P(x,y)=P(9k1k+1,8k+3k+1)

It is gien that point P lies on the line xy+2=0 ,
Thus,

(9k1k+1)(8k+3k+1)+2=0
9k18k3=2(k+1)
3k=2
k=23
So , the value of k is 23


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