Chapter 13.5, Problem 16PSC

To determine

To find:The minimum distance from H to J to K.

Answer to Problem 16PSC

The minimum distance from H to J to K is 28.3.

Explanation of Solution

Given:

The points is,

  $\begin{array}{l}H=\left(10,2\right)\\ K=\left(18,17\right)\end{array}$

Calculation:

According to the given question the slope of HK and HJ are equal. So,

  $\begin{array}{l}\frac{17-2}{-14-10}=\frac{y-2}{2-10}\\ 8y-16=40\\ y=7\end{array}$

Calculate the distance JH.

  $\begin{array}{c}\text{JH}=\sqrt{{\left(7-2\right)}^2+{\left(2-10\right)}^2}\\ =\sqrt{89}\end{array}$

Calculate the distance JK.

  $\begin{array}{c}\text{JK}=\sqrt{{\left(18-2\right)}^2+{\left(17-7\right)}^2}\\ =\sqrt{356}\end{array}$

Thus, the minimum distance from H to J to K is 28.3.