Question

Determine the points are collinear (1,2) (2,3) and (-2,-11)

Answer 1

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 $\Delta ABC$ must be 0.

Area of $\Delta ABC$,

$Area=\dfrac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|$

$Area=\dfrac{1}{2}|1(3-(-11))+2(-11-2)+(-2)(2-3)|$

$Area=\dfrac{1}{2}|(3+11)+2(-13)-2(-1)|$

$Area=\dfrac{1}{2}|14-26+2|$

$Area=\dfrac{1}{2}|-10|$

$Area=\dfrac{1}{2}(10)$

$Area=5\neq 0$

Therefore, the given points are not collinear.