Question

Find the value of $m$ if the points $(5,1),(2,3)$ and $(8,2m)$ are collinear.

• A. $-1$
• B. $\frac{1}{2}$
• C. $-\frac{1}{2}$
• D. $2$

Answer 1

Answer: (C)

$-\frac{1}{2}$

If three points are collinear, then the area of the triangle formed by taking these points as vertices should zero.

Area $=\frac{1}{2}$[$5(3-2m)+2(2m-1)+8(1-3)]$......(using determinant formula of area of triangle)

$=\frac{1}{2}$[$15-10m+4m-2+(-16)]$

$=\frac{1}{2}$ {$15-18-6m$}

$=\frac{1}{2}$$(-3-6m)=0$

$\Rightarrow (3+6m)=0$

$m=-\frac{1}{2}$.