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Question

If P is a point lying on the line segment joining Q(1,1) and R(4,1) such that PQ=37QR, then find the coordinates of P.


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Solution

Compute the required coordinates:

Given,

Q=(1,1)

R=(4,1)

P lies on QR.

PQ=37QR

So, PR=1-37

PR=47QR

PQ:PR=3:4

Therefore, P divides QR in ratio of 3:4.

Using 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

P=3×4+4×13+4,3×1+4×13+4

=167,1

Hence the coordinates of P is 167,1.


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