Question

Show that the points $(-1,7),(3,-5),(4,-8)$ are collinear.

Answer 1

Let $A(-1,7),B(3,-5),C(4,-8)$ be the coordinates

The given points are said to be collinear if area of $△ABC=0$

$\Delta =\frac{1}{2}\left|\begin{array}{ccc}-1& 3& 1\\ 3& -5& 1\\ 4& -8& 1\end{array}\right|$

$=\frac{1}{2}[-1(-5+8)-7(3-4)+1(-24+20)]$

$=\frac{1}{2}[-1\left(3\right)-7(-1)+1(-4)]$

$=\frac{1}{2}[-3+7-4]=0$

Hence the given points are collinear.