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)

For three points A(x₁, y₁), B(x₂, y₂), C(x₃, y₃)



(i)

Collinear points mean that the points lie on a straight line. So,

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 – 7 k + 5 k + 10 – 9 = 0

-2 k + 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