Question

The value of m, if the points A(5,1), B(-2,-3), and C(8,2m) are collinear is:

• A. $\frac{19}{17}$
• B. $\frac{19}{15}$
• C. $\frac{19}{14}$
• D. $\frac{15}{14}$

Answer 1

The correct option is C

$\frac{19}{14}$

Given, points A, B and C are collinear.

Then, slope of the line segment AB = slope of the line segment BC

We know that , Slope(m) of the line formed by joining the points $(x_1,y_1)$ and $(x_2,y_2)$ is given by

$m=\frac{y_2-y_1}{x_2-x_1}$

So, slope of the line segment AB = slope of the line segment BC implies,

$\frac{-3-1}{-2-5}$ = $\frac{2m-(-3)}{8-(-2)}$

$⟹\frac{-4}{-7}=\frac{2m+3}{10}$

$⟹40=14m+21$

$\Rightarrow m=\frac{19}{14}$

Hence, the required value of m is $\frac{19}{14}$.