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)
(i) For collinear points, area of triangle formed by them is zero
Therefore, for points (7, - 2) (5, 1), and (3, k), area = 0
[7 (1 – k) + 5 (k+ 2) + 3 (-2 – 1) = 0
7 – 7k + 5k + 10 – 9 = 0
-2k + 8 = 0
k = 4
(ii) For collinear points, area of triangle formed by them is zero.
Therefore, for points (8, 1), (k, - 4), and (2, - 5), area = 0
[8 (-4+ 5) + k (-5- 1) + 2 (1+ 4) = 0
8 – 6k + 10 = 0
6k = 18
k = 3
2