Question

Find the value of m if the points A (5,2), B(0,-3) and C(8,m) are collinear
m= _

Answer 1

If A (5,2), B(0,-3) and C(8,m) are collinear, then the area of the triangle formed by A, B and C is zero.
$\therefore \frac{1}{2}\left[5\right(-3-m)+(0\left)\right(m-1)+8(2-(-3)\left)\right]=0$

$\Rightarrow \left[5\right(-3-m)-0(2m-1)+8(2+3\left)\right]=0$

$\Rightarrow [-15-5m+40]=0$
$\Rightarrow -5m+25=0$
$\Rightarrow m=\frac{25}{5}$
$\Rightarrow m=5$