Chapter 1.3, Problem 36E

To determine

To explain: whether it is possible for two perpendicular lines to both have positive slope.

Answer to Problem 36E

It is not possible.

Explanation of Solution

Given information:

Product of slopes of two non-vertical perpendicular lines is always $-1$ , i.e.

  $m_1\cdot m_2=-1$

Calculation:

The rules of multiplying the slopes a and b is as follows:

  $\begin{array}{l}\left(+a\right)\cdot \left(-b\right)=-c\\ \left(-a\right)\cdot \left(+b\right)=-c\\ \left(+a\right)\cdot \left(+b\right)=+c\\ \left(-a\right)\cdot \left(-b\right)=+c\end{array}$

In order for c to be negative, either of the slope value should be negative. If both the slopes are positive, the value of c cannot be negative. i.e.

  $\left(+m_1\right)\cdot \left(+m_2\right)\ne -1$ .

Therefore, it is not possible for two perpendicular lines to have a positive slope.