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.
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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 (3k−5k+1,5k+1k+1)
Fig. C - 9 Also B is (1, 5) and C is (7, -2). Area of ΔABC=12{x1(y2−y3)+x2(y3−y1)+x3(y1−y2)} =±2(given) or12{3x−5k+1(5+2)+(−2−5x+1k+1)+7(5k+1k+1−5)} =±2 or21k−35−7k−3−28=±4(k+1) ∴14k−66=4k+4 or14k−66=−4k−4 ∴10k=70or18k=62 ∴k=7or319