# Among the two given points A ( 4 , 4 ) and B ( 5 , 3 ) which one of them is closer to the third point C ( − 1 , − 3 ) .

### 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, Problem 103RE
To determine

## To calculate:Among the two given points A(4,4) and B(5,3) which one of them is closer to the third point C(−1,−3) .

Expert Solution

Point B(5,3) is closer to point C(1,3) .

### Explanation of Solution

Given information:

The three points A(4,4) , B(5,3) and C(1,3)

Formula used:

The Distance denoted by say, D between any two given points say (x1,y1) and (x2,y2) is given as:

D=(x2x1)2+(y2y1)2

Calculation:

Consider the points A(4,4) and C(1,3)

Then in order to apply the distance formula the following should be known:

x1=4x2=4y1=1y2=3

Recall that for two points (x1,y1) and (x2,y2) is given as:

D=(x2x1)2+(y2y1)2

Therefore, if D1 denotes the distance between A(4,4) and C(1,3) then it is given as follows:

D1=(14)2+(34)2=(5)2+(7)2=25+49=74

Now, consider the points B(5,3) and C(1,3)

Then in order to apply the distance formula the following should be known:

x1=5x2=3y1=1y2=3

Recall that for two points (x1,y1) and (x2,y2) is given as:

D=(x2x1)2+(y2y1)2

Therefore, if D2 denotes the distance between B(5,3) and C(1,3) then it is given as follows:

D2=(15)2+(33)2=(6)2+(6)2=36+36=72

Clearly as 7472

That is D1D2

Using the fact that lesser the distance, closer the point.

Hence, B(5,3) is closer to C(1,3)

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