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Question
If the points A (2,3), B (4,k ) and C (6,-3) are collinear, find the value of k.
Solution
The given points are A (2,3), B (4,k ) and C (6,-3)
`Here , (x_1 = 2 , y_1 =3) , (x_2 =4, y_2 =k) and (x_3 = 6, y_3=-3)`
It is given that the points A, B and C are collinear. Then,
`x_1(y_2 -y_3 )+x_2 (y_3-y_1)+x_3 (y_1-y_2)=0`
⇒ 2 (k+3) + 4 (-3-3) + 6 (3-k) = 0
⇒ 2k + 6 - 24 +18 -6k =0
⇒ - 4k = 0
⇒ k =0
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