Question

Question 2 (ii)
Find the value of 'k', for which the following points are collinear.
(ii) (8, 1), (k, -4), (2, -5)

Answer 1

For collinear points, area of triangle formed by them is zero.
Therefore, for points (8, 1), (k, - 4) and (2, - 5), area = 0
Area of a triangle
= $\frac{1}{2}\left\{x_1\right(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2\left)\right\}$
=$\frac{1}{2}[8\{-4-(-5\left)\right\}+k\left\{\right(-5)-(1\left)\right\}+2\{1-(-4\left)\right\}]=0$
=$8-6k+10=0$
=$6k=18$
=$k=3$