Show that the points $(a + 5,a - 4),(a - 2,a + 3)$ and $(a,a)$ do not lie on a straight line for any value of $a$.

Given, the points are $(a + 5,a - 4),(a - 2,a + 3)$ and $(a,a)$.

$\therefore$ $\Delta = \frac{1}{2}\left| {\begin{array}{cccccccccccccccccccc}{a + 5}&{a - 4}&1\\{a - 2}&{a + 3}&1\\a&a&1\end{array}} \right|$

$= \frac{1}{2}\left| {\begin{array}{rrrrrrrrrrrrrrrrrrrr}5&{ - 4}&0\\{ - 2}&3&0\\a&a&1\end{array}} \right|$ and $\left. {{R_2} \to {R_2} - {R_3}} \right]$

$= \frac{1}{2}[1(15 - 8)]$

$\Rightarrow$ $= \frac{7}{2} \ne 0$

Hence, given points form a triangle i.e., points do not lie in a straight line.