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.

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