Chapter 7.1, Problem 74STP

To determine

To find: The slope of a straight line which represents the flight of a second bird that flew perpendicular to the first bird.

Answer to Problem 74STP

The slope of a straight line which represents the flight of a second bird that flew perpendicular to the first bird is $\left(-2\right)$ .

Explanation of Solution

Given information:

The coordinates of the line are $\left(1,2\right)$ and $\left(5,4\right)$ .

Calculation:

Consider the given figure.

Let, the coordinates of C from the above given figure is:

  $\left(x_1,y_1\right)=\left(1,2\right)$

The coordinates of D from the above given figure is:

  $\left(x_2,y_2\right)=\left(5,4\right)$

The formula to determine equation of slope for two point form straight line is:

  $m=\frac{y_2-y_1}{x_2-x_1}$

Substitute $1$ for $x_1$ , $2$ for $y_1$ , $5$ for $x_2$ and $4$ for $y_2$ in the above expression.

  $\begin{array}{c}m=\frac{4-2}{5-1}\\ =\frac{2}{4}\\ =\frac{1}{2}\end{array}$

Formula for slope for one line perpendicular to the other, where $m_1$ and $m_2$ are their respective slopes is:

  $m_1\times m_2=-1$

To determine the slope of the line through which second bird flew perpendicular to one bird, substitute $\frac{1}{2}$ for $m_1$ in the above expression.

  $\begin{array}{c}\left(\frac{1}{2}\right)\times m_2=-1\\ m_2=-1\times 2\\ =-2\end{array}$

Therefore, the slope of a straight line which represents the flight of a second bird that flew perpendicular to the first bird is $\left(-2\right)$ .