Chapter 13, Problem 14RP

To determine

To find: The value of $k$ .

Answer to Problem 14RP

The value of the $k$ is $\pm 2$ .

Explanation of Solution

Given:

The given points are $\left(2,1\right),\left(4,0\right)$ and $\left(-4,k^2\right)$ are collinear.

Calculation:

The formula to determine the slope of the line is of the form,

  $m=\frac{y_2-y_1}{x_2-x_1}$

The slope between the points $\left(2,1\right),\left(4,0\right)$ is,

  $\begin{array}{c}m=\frac{0-1}{4-2}\\ =-\frac{1}{2}\end{array}$

The slope between the points $\left(4,0\right),\left(-4,k^2\right)$ is,

  $\begin{array}{l}m=\frac{k^2-0}{-4-4}\\ -\frac{1}{2}=-\frac{k^2}{8}\\ k=\sqrt{4}\\ k=\pm 2\end{array}$