# The closer point among P ( 3 , 1 ) and Q ( − 1 , 3 ) to the point R ( − 1 , − 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 35E
To determine

## To calculate: The closer point among P(3,1) and Q(−1,3) to the point R(−1,−1) .

Expert Solution

Thecloser point tothe point R(1,1) is Q(1,3) .

### Explanation of Solution

Given information:

The points P(3,1) and Q(1,3) .

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 P(3,1) and Q(1,3) . Also the point R(1,1) .

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 P(3,1) and R(1,1) .

d(R,P)=(13)2+(11)2=16+4=20=4.47

Next evaluate the distance between Q(1,3) and R(1,1) .

d(Q,R)=(1(1))2+(13)2=16=4

Observe that d(R,P)>d(Q,P) .

That is the distance between the point Q(1,3) and the R(1,1) is less than the distance the point P(3,1) and the R(1,1) .

Therefore, the point Q(1,3) is near to R(1,1) .

Thus, the closer point to the point R(1,1) is Q(1,3) .

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