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Question

A(1,1) and B(2,3) are two points and D is a point on AB produced such that AD=3AB. If the coordinates of D are given by (p,q) then |p+q|=?

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Solution

Given: AD=3AB

AB+BD=3AB

Therefore, BD=2AB

Thus, D divides AB externally in the ratio AD:BD=3:2
Using the section formula, if a point (x,y) divides the line joining the points
(x1,y1) and (x2,y2)externally in the ratio m:n, then (x,y)=(mx2nx1mn,my2ny1mn)
Substituting (x1,y1)=(1,1) and (x2,y2)=(2,3) and m=3,n=2 in the section formula, we get
D=(3(2)2(1)32,3(3)2(1)32)=(4,11)


So, |p+q|=|411|=|7|=7

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