Find the value of $k$, if the points $A( 8,\ 1),\ B( 3,\ -4)$ and $C( 2,\ k)$ are collinear.

Given: Points $A( 8,\ 1),\ B( 3,\ -4)$ and $C( 2,\ k)$ are collinear.

To do: To find the value of $k$.

Solution:

Given points are: $A( 8,\ 1),\ B( 3,\ -4)$ and $C( 2,\ k)$

Two points can be collinear if their slopes are equal

$\Rightarrow$ Slope of $AB=$ Slope of $BC$

We have, slope between two point $=( \frac{y_2-y_1}{x_2-x_1})$

$\Rightarrow$ Slope of $AB=$ Slope of $BC$

$\Rightarrow \frac{-4-1}{3-8}=\frac{k-( -4)}{2-3}$

$\Rightarrow \frac{-5}{-5}=\frac{k+4}{-1}$
​
$\Rightarrow k+4=-1$

$\Rightarrow k=-5$

Thus, for $k=-5$ the given points are collinear.
 

Updated on: 10-Oct-2022

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