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Question

Find the abscissa of the point which divides the line segment joining the points (6,3) and (4,5) in the ratio 3:2 internally.

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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) internally in the ratio m:n, then (x,y)=(mx2+nx1m+n,my2+ny1m+n)
Substituting (x1,y1)(6,3) and (x2,y2)(4,5) and m=3,n=2 in the section formula, we get the point as,


(x,y)=(3(4)+2(6)3+2,3(5)+2(3)3+2)=(12123+2,15+62+3)=(0,215)


The required abscissa is 0.


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