Coordinate Geometry-4
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Show that the points A(-9, 7); B(3, 3); C (6,2) are collinear.
Solution: AB = √ (-9 -3)2 + (7 - 3)2 = √(144 + 16) = √160
i.e. AB = √16 x 10 = 4 √10 ....................................................(1)
AC = √(-9 - 6)2 + (7 -2)2 = √(225 + 25) = √250
= √ 25 x 10 = 5 √10 ...........................................................(2)
BC = √(3 -6)2 + (3 - 2)2 = √(9 + 1) = √10 ........(3)
From (i), (ii) and (iii), it is seen that
AC = AB + BC since 5 √10 = 4 √10 + √10
Therefore, A, B and C are collinear.
