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Question

# If A & B are the points (âˆ’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 theline joining the points (x1,y1) and (x2,y2)externally in the ratio m:n, then (x,y)=(mx2−nx1m−n,my2−ny1m−n)Since, AC=2BC=>ACBC=21Substituting (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)2−1,2(1)−1(4)2−1)=(7,−2)

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