Question

Find the value of $k$, if points $(10,14),(-3,3)$, and $(k,-8)$ are collinear.

• A. 16
• B. 18
• C. -18
• D. -16

Answer 1

Answer: (D)

Let the points be $A=(10,14),B=(-3,3)$ and $C=$ $(k,-8)$
Given, they are collinear $\Rightarrow$ The slopes are same.
$\Rightarrow \text{ Slope of }AB=\text{ Slope of }BC$
$\Rightarrow \frac{3-14}{-3-10}=\frac{-8-3}{k+3}$
$\Rightarrow \frac{-11}{-13}=\frac{-11}{k+3}$
$\Rightarrow k+3=-13$
$\Rightarrow k=-16.$