Chapter 4.3, Problem 41PPS

To determine

Whether the pole is perpendicular to the line through the pottery and the hair accessories.

Answer to Problem 41PPS

The pole is perpendicular to the joining pottery and hair accessories

Explanation of Solution

Given information:

In the ruins of an ancient civilization, an archaeologist found pottery at $\left(2,6\right)$ and hair accessories at $\left(4,-1\right)$ . A pole is found with one end at $\left(7,10\right)$ and the other end at $\left(14,12\right)$ .

Calculation:

The slope of the line $m_1$ joining the points $R\left(2,6\right)$ and $S\left(4,-1\right)$

  $\begin{array}{c}{m}_1=\frac{-1-6}{4-2}\\ =-\frac{7}{2}\end{array}$

The slope of the line $m_2$ joining the points $J\left(7,10\right)$ and $k\left(14,12\right)$

  $\begin{array}{c}{m}_2=\frac{12-10}{14-7}\\ =\frac{2}{7}\end{array}$

Here $m_1=-\frac{7}{2}$ is negative reciprocal of $m_2=\frac{2}{7}$

Therefore, the pole is perpendicular to the joining pottery and hair accessories.