# If line q has a slope of 2, what is the slope of any line perpendicular to q?

Mar 5, 2018

$\setminus q \quad \setminus q \quad \setminus \quad \text{slope of any line perpendicular to} \setminus q \setminus = \setminus - \frac{1}{2.}$

#### Explanation:

$\text{Recall that if two lines are perpendicular to each other then}$
$\text{their slopes are negative reciprocals of each other or one is}$
$\text{vertical (having no slope) and the other is horizontal (having}$
$\text{zero slope).}$

$\text{Our line" \ q, "has slope 2, and so is neither vertical nor horizontal.}$
$\text{So, any line perpendicular to" \ q \ "has slope that is the negative}$
$\text{reciprocal of the slope of line} \setminus q .$

$\text{So let" \ p \ "be a line perpendicular to line} \setminus q .$

$\text{Then we have:}$

$\setminus q \quad \setminus q \quad \setminus \quad \text{slope of" \ p \ = \ "negative reciprocal of slope of line} \setminus q$

$\setminus q \quad \setminus q \quad \setminus q \quad \setminus q \quad \setminus q \quad \setminus q \quad \setminus \quad \setminus = \setminus \text{negative reciprocal of} \setminus \left(2\right)$

$\setminus q \quad \setminus q \quad \setminus q \quad \setminus q \quad \setminus q \quad \setminus q \quad \setminus \quad \setminus = \setminus \text{negative of} \setminus \left(\frac{1}{2}\right)$

$\setminus q \quad \setminus q \quad \setminus q \quad \setminus q \quad \setminus q \quad \setminus q \quad \setminus \quad \setminus = \setminus - \frac{1}{2.}$

$\text{Thus:}$

$\setminus q \quad \setminus q \quad \setminus q \quad \setminus q \quad \setminus q \quad \setminus q \quad \setminus q \quad \setminus q \quad \setminus \quad \text{slope of} \setminus p \setminus = \setminus - \frac{1}{2.}$

$\text{So:}$

$\setminus q \quad \setminus q \quad \setminus q \quad \text{slope of any line perpendicular to} \setminus q \setminus = \setminus - \frac{1}{2.}$

$\text{This is our answer.}$