# The formula of distance between two coordinates and the distance between the given coordinates. ### 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 2E
To determine

## To fill: The formula of distance between two coordinates and the distance between the given coordinates.

Expert Solution

The coordinate of the point is (3,5) and distance between the points (1,2) and (7,0) is 10.

### Explanation of Solution

Given:

The given coordinates are (a,b) and (c,d) .

Formula used:

d(A,B)=(x2x1)2+(y2y1)2

Where, (x1,y1) and (x2,y2) are coordinate of point A and B respectively.

Calculation:

Section1:

Substituting the value of given coordinates in the formula to find the distance between them.

Substitute a for x1 , b for y1 , c for x2 and d for y2 .

d=(ca)2+(db)2

Therefore, distance between the points (a,b) and (c,d) is (ca)2+(db)2 .

Section2:

The given coordinates are (1,2) and (7,10) .

Substituting the value of given coordinates in the formula to find the distance between them.

Substitute 1 for x1 2 for y1 , 7 for x2 and 0 for y2 .

d=(71)2+(102)2=(6)2+(8)2=36+64=10

Therefore, distance between the points (1,2) and (7,0) is 10.

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