# The closer point among A ( 6 , 7 ) and B ( − 5 , 8 ) to 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 33E
To determine

## To calculate: The closer point among A(6,7) and B(−5,8) to the origin.

Expert Solution

Thecloser point to originis A(6,7) .

### Explanation of Solution

Given information:

The points A(6,7) and B(5,8) .

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(6,7) and B(5,8) .

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 .

Denote the origin as O(0,0) .

Evaluate the distance between A(6,7) and O(0,0) .

d(A,O)=(06)2+(07)2=36+49=85

Next evaluate the distance between B(5,8) and O(0,0) .

d(B,O)=(0(5))2+(08)2=25+64=89

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

That is the distance between the point A(6,7) and the origin is less than the distance the point B(5,8) and the origin.

Therefore, the point A(6,7) is near to origin.

Thus, the closer point to origin is A(6,7) .

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