Question

Find the value of m if the points A(5, 1), B(-2, -3) and C(8, 2m) are collinear
m = ___
(Enter in the form a/b if you obtain a fraction)

Answer 1

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

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

$\Rightarrow [-15-10m-4m+2+32]=0$
$\Rightarrow -14m+19=0$
$\Rightarrow m=\frac{19}{14}$