Question

Check whether the points $X(-1,3),Y(8,-3)$ and $Z(2,1)$ are collinear.

Answer 1

Given three points are $X(-1,3),Y(8,-3)$ and $Z(2,1)$.

If the three points are collinear, then the area of triangle $=0$.

$\left[\begin{array}{ccc}{x}_1& y_1& 1\\ x_2& y_2& 1\\ x_3& y_3& 1\end{array}\right]=0$

By substituting values, we have

$\left[\begin{array}{ccc}-1& 3& 1\\ 8& -3& 1\\ 2& 1& 1\end{array}\right]=0$

Taking LHS, we have

$=-1(-3-1)-3(8-2)+1(8+6)$

$=-1(-4)-3\left(6\right)+1\left(14\right)$

$=4-18+14$

$=-14+14$

$=0$

Therefore, the given points are collinear.