# The closer point among C ( − 6 , 3 ) and D ( 3 , 0 ) to the point E ( − 2 , 1 ) . ### 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 34E
To determine

## To calculate: The closer point among C(−6,3) and D(3,0) to the point E(−2,1) .

Expert Solution

Thecloser point tothe point E(2,1) is C(6,3) .

### Explanation of Solution

Given information:

The points C(6,3) and D(3,0) .

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 C(6,3) and D(3,0) . Also the point E(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 C(6,3) and E(2,1) .

d(C,E)=(2(6))2+(13)2=16+4=20

Next evaluate the distance between D(3,0) and E(2,1) .

d(D,E)=(23)2+(10)2=25+1=26

Observe that d(D,E)>d(C,E) .

That is the distance between the point C(6,3) and the E(2,1) is less than the distance the point D(3,0) and the E(2,1) .

Therefore, the point C(6,3) is near to E(2,1) .

Thus, the closer point to the point E(2,1) is C(6,3) .

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