Chapter 13.7, Problem 29WE

To determine

To find : an equation of line described

Answer to Problem 29WE

The equation is $5x+3y-34=0$

Explanation of Solution

Given information :

Perpendicular bisector of segment joining $\left(0,0\right)$ and $\left(10,6\right)$

Formula used :

  $y-y_1=m\left(x-x_1\right)$

Calculation :

The point of bisection

  $\begin{array}{l}=\left(\frac{0+10}{2},\frac{0+6}{2}\right)\\ =\left(5,3\right)\end{array}$

The slope of segment

  $\begin{array}{l}=\frac{6-0}{10-0}\\ =\frac{3}{5}\end{array}$

Therefore, the slope is $\frac{3}{5}$ .

The required line has slop $m_2=-\frac{1}{m_1}=-\frac{5}{3}$

Using $\left(5,3\right)$ , the equation is

  $\begin{array}{l}y-3=-\frac{5}{3}\left(x-5\right)\\ y=-\frac{5}{3}x+\frac{25}{3}+3\\ y=-\frac{5}{3}x+\frac{34}{3}\\ 3y=-5x+34\\ 5x+3y-34=0\end{array}$

Hence, the equation is $5x+3y-34=0$ .