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Question

If A & B are the points (3,4) and (2,1), then the coordinates of the point C on produced AB such that AC=2BC are

A
(2,4)
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B
(3,7)
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C
(7,2)
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D
(12,52)
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Solution

The correct option is C (7,2)

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)
Since, AC=2BC=>ACBC=21
Substituting (x1,y1)=(3,4) and (x2,y2)=(2,1) and m=2,n=1 in the section formula, we get
C=(2(2)1(3)21,2(1)1(4)21)=(7,2)


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