10th Edition

ISBN: 9780134672090

Author: Demana

Publisher: PEARSON

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Expert Solution & Answer

Chapter P.4, Problem 59E

Solution

a.

Is it possible for two lines with positive slopes to be perpendicular?

No

Given:

Two lines with positive slope.

Concept Used:

The slope-intercept form of a line is y=mx+b, where m is the slope of the line and b is the y -intercept of the line.

Slope of the line passing through the points x1,y1 and x2,y2 is given by m=y2−y1x2−x1

The slopes of two perpendicular lines are negative reciprocal of each other.

Calculation:

Since the slopes of two perpendicular lines is negative reciprocal of each other. So, if a line has a positive slope m , then the line perpendicular to it must have a slope that is equal to negative reciprocal of m , that is, −1m .

Thus, it is not possible for two lines with positive slopes to be perpendicular.

b.

Is it possible for two lines with negative slopes to be perpendicular?

No

Given:

Two lines with negative slope.

Concept Used:

The slope-intercept form of a line is y=mx+b, where m is the slope of the line and b is the y -intercept of the line.

Slope of the line passing through the points x1,y1 and x2,y2 is given by m=y2−y1x2−x1

The slopes of two perpendicular lines are negative reciprocal of each other.

Calculation:

Since the slopes of two perpendicular lines is negative reciprocal of each other. So, if a line has a negative slope −m , then the line perpendicular to it must have a slope that is equal to negative reciprocal of −m , that is, −1−m=1m .

Thus, it is not possible for two lines with negative slopes to be perpendicular.

Chapter P.4, Problem 58E

Chapter P.4, Problem 60E

Chapter P Solutions

PRECALCULUS:GRAPHICAL,...-NASTA ED.

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Solution Summary: The author explains that the slopes of two perpendicular lines are negative reciprocal of each other.

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Chapter P Solutions