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 33E
To determine

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

Expert Solution

Answer to Problem 33E

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) .

Have a homework question?

Subscribe to bartleby learn! Ask subject matter experts 30 homework questions each month. Plus, you’ll have access to millions of step-by-step textbook answers!