BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071
BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

Solutions

Chapter 1.8, Problem 10E

  (a)

To determine

To calculate: The distance between the pair of points that are graphed below.

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 1.8, Problem 10E , additional homework tip  1

Expert Solution

Answer to Problem 10E

The distance between the pair of points is 5 units

Explanation of Solution

Given information:

The points are depicted graphically,

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 1.8, Problem 10E , additional homework tip  2

Formula used:

Distance d(A,B) between two points A=(x1,y1) and B=(x2,y2) in the Cartesian plane is denoted by d(A,B)=(x2x1)2+(y2y1)2 .

Calculation:

Consider the points that are depicted graphically,

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 1.8, Problem 10E , additional homework tip  3

The two points are A(2,2) and B(2,1) .

Recall that the distance d(A,B) between two points A=(x1,y1) and B=(x2,y2) in the Cartesian plane is denoted by d(A,B)=(x2x1)2+(y2y1)2 .

Evaluate the distance between A(2,2) and B(2,1) .

  d(A,B)=(22)2+(12)2=16+9=25=5

Thus, the distance between the pair of points is 5 units.

  (b)

To determine

To calculate: The midpoint of the segment that joins the pair of points that are graphed below.

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 1.8, Problem 10E , additional homework tip  4

Expert Solution

Answer to Problem 10E

The midpoint of the segment that joins the pair of points is (0,12) .

Explanation of Solution

Given information:

The points are depicted graphically,

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 1.8, Problem 10E , additional homework tip  5

Formula used:

Midpoint of the segment that joins two points A=(x1,y1) and B=(x2,y2) in the Cartesian plane is denoted by (x1+x22,y1+y22) .

Calculation:

Consider the points that are depicted graphically,

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 1.8, Problem 10E , additional homework tip  6

The two points are A(2,2) and B(2,1) .

Recall that the midpoint of the segment that joins two points A=(x1,y1) and B=(x2,y2) in the Cartesian plane is denoted by (x1+x22,y1+y22) .

Evaluate the midpoint of the segment that joins A(2,2) and B(2,1) .

  (x1+x22,y1+y22)=(2+(2)2,2+(1)2)=(02,12)=(0,12)

Thus, the midpoint of the segment that joins the pair of points is (0,12) .

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