BIG IDEAS MATH Integrated Math 1: Student Edition 2016

16th Edition

ISBN: 9781680331127

Author: HOUGHTON MIFFLIN HARCOURT

Publisher: Houghton Mifflin Harcourt

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Question

Chapter 4.3, Problem 15E

To determine

which of the lines are parallel or perpendicular.

Expert Solution & Answer

Answer to Problem 15E

The lines $a, b and c$ are not parallel to each other.

The lines $b and c$ are perpendicular to each other.

Explanation of Solution

Given:

Line a passes through (-2,1) and (0,3)

Line b passes through (4,1) and (6,4)

Line c passes through (1,3) and (4,1)

Calculation:

Consider the lines $a,b, and c$ such that the coordinates forline $a are (−2,1) and (0,3)$ , the coordinates for line $b are (4,1) and (6,4)$ and the coordinates for line $c are (1,3) and (4,1)$ .

The objective is to determine which lines are parallel or perpendicular.

To determine whether the lines are parallel or perpendicular, find the slopes of lines $a, b, and c$ .

The slope of a line is the ratio of difference of $y coordinate to x coordinate$ .

Therefore, the slope of line $a$ is,

$ma=1−3−2−0=−2−2=1$

The slope of line $b$ is,

$mb=1−44−6=−3−2=32$

Similarly, the slope ofline $c$ is,

$mc=3−11−4=2−3=−23$

Since the slopes of line $a, b and c$ are different, therefore, lines $a, b and c$ are not parallel to each other.

But, the slope of lines $b and c$ is negative inverse of each other.

That is,

$mc=−6−(−1)−3−0=−5−3=53a, b and cmbmc=32(−23)mbmc=−1$

Therefore, the lines $b and c$ areperpendicular to each other.

Conclusion:

The lines $a, b and c$ are not parallel to each other.

The lines $b and c$ are perpendicular to each other.

Chapter 4.3, Problem 14E

Chapter 4.3, Problem 16E

Chapter 4 Solutions

BIG IDEAS MATH Integrated Math 1: Student Edition 2016

Ch. 4.1 - Prob. 1E Ch. 4.1 - Prob. 2E Ch. 4.1 - Prob. 3E Ch. 4.1 - Prob. 4E Ch. 4.1 - Prob. 5E Ch. 4.1 - Prob. 6E Ch. 4.1 - Prob. 7E Ch. 4.1 - Prob. 8E Ch. 4.1 - Prob. 9E Ch. 4.1 - Prob. 10E

Ch. 4.1 - Prob. 11E Ch. 4.1 - Prob. 12E Ch. 4.1 - Prob. 13E Ch. 4.1 - Prob. 14E Ch. 4.1 - Prob. 15E Ch. 4.1 - Prob. 16E Ch. 4.1 - Prob. 17E Ch. 4.1 - Prob. 18E Ch. 4.1 - Prob. 19E Ch. 4.1 - Prob. 20E Ch. 4.1 - Prob. 21E Ch. 4.1 - Prob. 22E Ch. 4.1 - Prob. 23E Ch. 4.1 - Prob. 24E Ch. 4.1 - Prob. 25E Ch. 4.1 - Prob. 26E Ch. 4.1 - Prob. 27E Ch. 4.1 - Prob. 28E Ch. 4.1 - Prob. 29E Ch. 4.1 - Prob. 30E Ch. 4.1 - Prob. 31E Ch. 4.1 - Prob. 32E Ch. 4.1 - Prob. 33E Ch. 4.1 - Prob. 34E Ch. 4.1 - Prob. 35E Ch. 4.1 - Prob. 36E Ch. 4.1 - Prob. 37E Ch. 4.1 - Prob. 38E Ch. 4.1 - Prob. 39E Ch. 4.1 - Prob. 40E Ch. 4.1 - Prob. 41E Ch. 4.1 - Prob. 42E Ch. 4.1 - Prob. 43E Ch. 4.1 - Prob. 44E Ch. 4.1 - Prob. 45E Ch. 4.2 - Prob. 1E Ch. 4.2 - Prob. 2E Ch. 4.2 - Prob. 3E Ch. 4.2 - Prob. 4E Ch. 4.2 - Prob. 5E Ch. 4.2 - Prob. 6E Ch. 4.2 - Prob. 7E Ch. 4.2 - Prob. 8E Ch. 4.2 - Prob. 9E Ch. 4.2 - Prob. 10E Ch. 4.2 - Prob. 11E Ch. 4.2 - Prob. 12E Ch. 4.2 - Prob. 13E Ch. 4.2 - Prob. 14E Ch. 4.2 - Prob. 15E Ch. 4.2 - 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