Question

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

• A. 2
• B. 3
• C. 4
• D. 5

Answer 1

The correct option is D 5

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.

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

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