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Question

If A(−2,5) and B(3,2) are the points on a straight line. If AB is extended to ′C′ such that AC=2BC, then the co-ordinates of ′C′ are ____

A
(12,32)
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B
(72,12)
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C
(8,1)
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D
(1,8)
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Solution

The correct option is C (8,1)

Given points are A(2,5) and B(3,2)
ACBC=21 , C divides line segment AB externally.
If A(x1,y1) and B(x2,y2) be two end points of a line segment, then the coordinates of the point P(x,y) that divides the line segment externally in the ratio m:n is (mx2nx1mn,my2ny1mn).
Thus, the coordinates of C are (2(3)1(2)21,2(2)1(5)21).
=(6+21,451)
=(8,1)

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