Question

For what value of a the point (a, 1), (1, -1) and (11, 4) are collinear?

Answer 1

If three points are collinear, the area of the triangle formed by them is zero.

Here, area of triangle = $\frac{1}{2}|(x_1{y}_2-y_1{x}_2)+(x_2{y}_3-y_2{x}_3)+(x_3{y}_1-y_3{x}_1)|=0$

$\Rightarrow (x_1{y}_2-y_1{x}_2)+(x_2{y}_3-y_2{x}_3)+(x_3{y}_4-y_3{x}_4)=0$

$\Rightarrow (-a-1)+(4+11)+(11-4a)=0$

$\Rightarrow a=5$