valu of k th le points (-k + 1,2k),(k,2-2k) and (-4 - k,2k) are collinear
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Hi !
if the points are collinear ,
-k+ 1 (2 - 2k - 2k) + k ( 2k - 2k) + -4 - k( 2k - { 2 - 2k} ) = 0
-k + 1 ( 2 - 4k) + k(0) - 4 - k(4k - 2) = 0
-2k + 4k² + 2 - 4k + 0 -16k + 8 - 4k² + 2k = 0
-4k - 16k + 2 + 8 = 0
-20k + 10 = 0
-20k = -10
k = -10/-20
= 1/2
= 0.5
if the points are collinear ,
-k+ 1 (2 - 2k - 2k) + k ( 2k - 2k) + -4 - k( 2k - { 2 - 2k} ) = 0
-k + 1 ( 2 - 4k) + k(0) - 4 - k(4k - 2) = 0
-2k + 4k² + 2 - 4k + 0 -16k + 8 - 4k² + 2k = 0
-4k - 16k + 2 + 8 = 0
-20k + 10 = 0
-20k = -10
k = -10/-20
= 1/2
= 0.5
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