# The distance between the point ( 7 , 3 ) and the origin is same as distance betweenthe point ( 3 , 7 ) and the origin.

### Precalculus: Mathematics for Calcu...

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

### Precalculus: Mathematics for Calcu...

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

#### Solutions

Chapter 1.8, Problem 36E

(a)

To determine

## To show: The distance between the point (7,3) and the origin is same as distance betweenthe point (3,7) and the origin.

Expert Solution

### Explanation of Solution

Given information:

The points (7,3) and (3,7) .

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 provided set of points (7,3) and (3,7) .

Denote the origin as O(0,0) .

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(7,3) and O(0,0) .

d(A,O)=(07)2+(03)2=49+9=58

Evaluate the distance between B(3,7) and O(0,0) .

d(B,O)=(03)2+(07)2=9+49=58

Observe that d(B,O)=d(A,O) .

That is the distance between the point (7,3) and the origin is same as the distance the point (3,7) and the origin.

Hence, it is shown that the distance between the point (7,3) and the origin is same as distance betweenthe point (3,7) and the origin.

(b)

To determine

Expert Solution

### Explanation of Solution

Given information:

The points (a,b) and (b,a) .

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 provided set of points (a,b) and (b,a) .

Denote the origin as O(0,0) .

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(a,b) and O(0,0) .

d(A,O)=(0a)2+(0b)2=a2+b2

Evaluate the distance between B(b,a) and O(0,0) .

d(B,O)=(0b)2+(0a)2=b2+a2=a2+b2

Observe that d(B,O)=d(A,O) .

That is the distance between the point (a,b) and the origin is same as the distance the point (b,a) and the origin.

Hence, it is shown that the distance between the point (a,b) and the origin is same as distance betweenthe point (b,a) and the origin.

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