Chapter 4.6, Problem 4PSA

To determine

To find: The slope of given line.

Answer to Problem 4PSA

  $-\frac{1}{2}$ .

Explanation of Solution

Given information:

  $\angle F$ is a right angle in below figure.

  

Concept used: Slope of two perpendicular lines are negative reciprocal of each other.

  $m_1=-\frac{1}{m_2}$ .

Calculation:

  

  $\angle F$ is a right angle. This means $\overleftrightarrow{EF}\perp \overleftrightarrow{FH}$ .

Therefore slope of line $\overleftrightarrow{FH}$ would be negative reciprocal of slope of line $\overleftrightarrow{EF}$ .

  $\begin{array}{l}\text{So, slope of line }\overleftrightarrow{EF}=\frac{y_2-y_1}{x_2-x_1}=\frac{3-7}{4-2}=-2\\ \text{And, slope of line }\overleftrightarrow{FH}=-\frac{1}{-2}=\frac{1}{2}\end{array}$ .

Hence, slope of line $\overleftrightarrow{FH}$ is $-\frac{1}{2}$ .