Question 2 In each of the following find the value of ‘k’, for which the points are collinear. (i) (7, − 2), (5, 1), (3, − k) (ii) (8, 1), (k, − 4), (2, − 5)
Class 10 - Math - Coordinate Geometry Page 170
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for collinearity slope should be constant throughout
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points are colinear , when ; area of triangle form by these points = 0
(1) area of ∆ = 1/2 { 7(1 + k) +5(-k +2) +3(-2 -1)}
0 = 7 + 7K - 5K + 10 -9
0 = 2K + 8
K = -4
(2) area of ∆ = 1/2 { 8( -4 + 5) + K(-5 -1)+2( 1 + 4) }
0 = 8 -6K + 10
K = 3
(1) area of ∆ = 1/2 { 7(1 + k) +5(-k +2) +3(-2 -1)}
0 = 7 + 7K - 5K + 10 -9
0 = 2K + 8
K = -4
(2) area of ∆ = 1/2 { 8( -4 + 5) + K(-5 -1)+2( 1 + 4) }
0 = 8 -6K + 10
K = 3
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