BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter B, Problem 6E

(a)

To determine

To calculate: To show that the points A(1,3)

  B(3,11) and C(5,15) are collinear by showing that |AB|+|BC|=|AC|

Expert Solution

Answer to Problem 6E

It isproved that points are collinear by showing that |AB|+|BC|=|AC|

Explanation of Solution

Given information: Points are A(1,3)

  B(3,11) and C(5,15)

Formula Used:

Distance between two points is given as

  D=(x2x1)2+(y2y1)2

Calculation:

Points are given as

  A(1,3)

  B(3,11) and C(5,15)

Length of AB is calculated as follows:

  |AB|=(3(1))2+(113)2|AB|=42+82|AB|=16+64|AB|=80|AB|=45

Length of BC is calculated as follows:

  |BC|=(53)2+(1511)2|BC|=22+42|BC|=4+16|BC|=20|BC|=25

Length of AC is calculated as follows:

  |AC|=(5(1))2+(153)2|AC|=62+122|AC|=36+144|AC|=180|AC|=65

Now, calculating |AB|+|BC| ,

  |AB|+|BC|=45+25|AB|+|BC|=65|AB|+|BC|=|AC|

Thus, points A, B and C are collinear

Conclusion:

Hence, its proved that points are collinear by showing that |AB|+|BC|=|AC|

(b)

To determine

To calculate: To show that the points A(1,3)

  B(3,11) and C(5,15) are collinear by using slopes

Expert Solution

Answer to Problem 6E

It isproved that points are collinear by showing that slopes are equal

Explanation of Solution

Given information: Points are A(1,3)

  B(3,11) and C(5,15)

Formula Used:

Slope of line joining two points is calculated as

  m=y2y1x2x1

Calculation:

Points are given as

  A(1,3)

  B(3,11) and C(5,15)

Slope of line AB is calculated as follows:

  mAB=1133(1)mAB=84mAB=2

Slope of line BC is calculated as follows:

  mBC=151153mBC=42mBC=2

Slope of line AC is calculated as follows:

  mAC=1535(1)mAC=126mAC=2

Since mAB=mBC=mAC=2

Thus, points A, B and C are collinear

Conclusion:

Hence, its proved that points are collinear by showing that slope of lines are equal

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