Question

For what value of $m$, the points $(3,5)$, $(m,6)$ and $\left(\begin{array}{c}\frac{1}{2},\frac{15}{2}\end{array}\right)$ are collinear?

• A. $9$
• B. $5$
• C. $3$
• D. $2$

Answer 1

The correct option is D $2$

As the points are collinear, the slope of the line joining any two points, should be same as the slope of the line joining two other points.
Slope of the line passing through points $(x_1,y_1)$ and $(x_2,y_2)$ = $\frac{y_2-y_1}{x_2-x_1}$
So, slope of the line joining $(3,5),(m,6)=$ Slope of the line joining $(3,5)$ and $(\frac{1}{2},\frac{15}{2})$

Therefore, $\frac{6-5}{m-3}=\frac{\frac{15}{2}-5}{\frac{1}{2}-3}$
$\Rightarrow \frac{1}{m-3}=-1$

$\Rightarrow m-3=-1$

$\Rightarrow m=2$