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Question

A line AB meets X-axis at A and Y-axis at B.P(4,1) divides AB in the ratio 1:2.
Find the coordinates of A and B
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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 coordinates of A and B be (a,0) and (0,b)
The coordinate of a point P(4,1) on AB divides it in the ratio 1:2.
i.e., AP:PB=1:2
By using section formula,
4=1×0+2×a1+2[x=m1x2+m2x1m1+m2]
12=2aa=6
and 1=1×b+2×01+2[y=m1y2+m2y1m1+m2]
3=b
Hence, Coordinate of A=(6,0)
and Coordinate of B=(0,3)

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