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

1 Answer
Mar 5, 2018

Answer:

# \qquad \qquad \quad "slope of any line perpendicular to" \ q \ = \ -1/2. #

Explanation:

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

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

# "So let" \ p \ "be a line perpendicular to line" \ q. #

# "Then we have:" #

# \qquad \qquad \quad "slope of" \ p \ = \ "negative reciprocal of slope of line" \ q #

# \qquad \qquad \qquad \qquad \qquad \qquad \quad \ = \ "negative reciprocal of" \ (2) #

# \qquad \qquad \qquad \qquad \qquad \qquad \quad \ = \ "negative of" \ (1/2) #

# \qquad \qquad \qquad \qquad \qquad \qquad \quad \ = \ -1/2. #

# "Thus:" #

# \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \quad "slope of" \ p \ = \ -1/2. #

# "So:" #

# \qquad \qquad \qquad "slope of any line perpendicular to" \ q \ = \ -1/2. #

# "This is our answer." #