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Question

A line segment AB is produced to C such that AC = 2AB. If the coordinates of A and B are (6,8) and (8,6) respectively, then the coordinates of C are
  1. (10,4)
  2. (5,2)
  3. (7,7)
  4. (8,7)

A
(8,7)
B
(10,4)
C
(5,2)
D
(7,7)
Solution
Verified by Toppr

The correct option is A (10,4)
Given that, a line segment AB is produced to C such that AC=2AB.
Also, the coordinates are A(6,8) and B(8,6).
To find out: The coordinates of the point C.

Let the coordinates of point C be (x,y).
Since, AC=2AB, the point C divides the line segment in the ratio 2:1 externally.

We know that, if a point P(x,y) divides a line segment joining A(x1,y1) and B(x2,y2) in the ratio m:n externally, then the coordinates of the point P are:
x=mx2nx1mn and y=my2ny1mn

Here, m=2, n=1, x1=6, y1=8 x2=8, y2=6

x=2(8)1(6)21 and y=2(6)1(8)21

x=1661 and y=1281

x=10 and y=4

Hence, the coordinates of the point C are (10,4).

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