   # Suppose we want to find the coordinates of the midpoint of a line segment. Let P ( x , y ) represent the midpoint of the line segment from A ( x 1 , y 1 ) to B ( x 2 , y 2 ) . Using the method from Problem 68, the formula for the x coordinate of the midpoint is x = x 1 + 1 2 ( x 2 − x 1 ) . This formula can be simplified algebraically to produce a simpler formula. x = x 1 + 1 2 ( x 2 − x 1 ) x = x 1 + 1 2 x 2 − 1 2 x 1 x = 1 2 x 1 + 1 2 x 2 x = x 1 + x 2 2 Hence the x coordinate of the midpoint can be interpreted as the average of the x coordinate of the endpoints of the line segment. A similar argument for the y coordinate of the midpoint gives the following formula. y = y 1 + y 2 2 For each of the pairs of points, use the formula to find the midpoint of the line segment between the points. (a) ( 3 , 1 ) and ( 7 , 5 ) (b) ( − 2 , 8 ) and ( 6 , 4 ) (c) ( − 3 , 2 ) and ( 5 , 8 ) (d) ( 4 , 10 ) and ( 9 , 25 ) (e) ( − 4 , − 1 ) and ( − 10 , 5 ) (f) ( 5 , 8 ) and ( − 1 , 7 ) ### Intermediate Algebra

10th Edition
Jerome E. Kaufmann + 1 other
Publisher: Cengage Learning
ISBN: 9781285195728

#### Solutions

Chapter
Section ### Intermediate Algebra

10th Edition
Jerome E. Kaufmann + 1 other
Publisher: Cengage Learning
ISBN: 9781285195728
Chapter 7.3, Problem 70PS
Textbook Problem
1 views

## Suppose we want to find the coordinates of the midpoint of a line segment. Let P ( x , y ) represent the midpoint of the line segment from A ( x 1 , y 1 ) to B ( x 2 , y 2 ) . Using the method from Problem 68, the formula for the x coordinate of the midpoint is x = x 1 + 1 2 ( x 2 − x 1 ) . This formula can be simplified algebraically to produce a simpler formula. x = x 1 + 1 2 ( x 2 − x 1 ) x = x 1 + 1 2 x 2 − 1 2 x 1 x = 1 2 x 1 + 1 2 x 2 x = x 1 + x 2 2 Hence the x coordinate of the midpoint can be interpreted as the average of the x coordinate of the endpoints of the line segment. A similar argument for the y coordinate of the midpoint gives the following formula. y = y 1 + y 2 2 For each of the pairs of points, use the formula to find the midpoint of the line segment between the points.(a) ( 3 , 1 ) and ( 7 , 5 ) (b) ( − 2 , 8 ) and ( 6 , 4 ) (c) ( − 3 , 2 ) and ( 5 , 8 ) (d) ( 4 , 10 ) and ( 9 , 25 ) (e) ( − 4 , − 1 ) and ( − 10 , 5 ) (f) ( 5 , 8 ) and ( − 1 , 7 )

To determine

a)

To find:

The midpoint of the line segment joining the points (3,1) and (7,5).

### Explanation of Solution

Formula used:

The formula to calculate the midpoint of line segment joining the points (x1,y1) and (x2,y2).

For x coordinate of midpoint,

x=x1+x22

For y coordinate of midpoint,

y=y1+y22

The midpoint will be (x1+x22,y1+y22)

Calculation:

Consider the points (3,1) and (7,5)

To determine

b)

To find:

The midpoint of the line segment joining the points (2,8) and (6,4).

To determine

c)

To find:

The midpoint of the line segment joining the points (3,2) and (5,8).

To determine

d)

To find:

The midpoint of the line segment joining the points (4,10) and (9,25).

To determine

e)

To find:

The midpoint of the line segment joining the points (4,1) and (10,5).

To determine

f)

To find:

The midpoint of the line segment joining the points (5,8) and (1,7).

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