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Question

The point A divides the join of P(-5, 1) and Q(3, 5) in the ratio k:1. Find the two values of k for which the area of ΔABC where B is (1, 5) and C is (7, -2) is equal to 2 units.
  1. undefined
  2. undefined
  3. undefined
  4. undefined

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Solution

Using section formula, the coordinates of point A which divides the join of P(-5, 1) and Q(3, 5) in the ratio k:1 is
(3k5k+1,5k+1k+1)

Fig. C - 9
Also B is (1, 5) and C is (7, -2).
Area of ΔABC=12{x1(y2y3)+x2(y3y1)+x3(y1y2)}
=±2 (given)
or 12{3x5k+1(5+2)+(25x+1k+1)+7(5k+1k+15)}
=±2
or 21k357k328=±4(k+1)
14k66=4k+4
or 14k66=4k4
10k=70 or 18k=62
k=7 or 319

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