Given:
The three points are (1,2), (2,3) and (-2,-11).
To find:
Whether the given points are collinear.
Solution:
Let as consider the three points are A(1,2), B(2,3) and C(-2,-11).
If these three points are collinear, then area of [tex]\Delta ABC[/tex] must be 0.
Area of [tex]\Delta ABC[/tex],
[tex]Area=\dfrac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|[/tex]
[tex]Area=\dfrac{1}{2}|1(3-(-11))+2(-11-2)+(-2)(2-3)|[/tex]
[tex]Area=\dfrac{1}{2}|(3+11)+2(-13)-2(-1)|[/tex]
[tex]Area=\dfrac{1}{2}|14-26+2|[/tex]
[tex]Area=\dfrac{1}{2}|-10|[/tex]
[tex]Area=\dfrac{1}{2}(10)[/tex]
[tex]Area=5\neq 0[/tex]
Therefore, the given points are not collinear.
