# To show that the mid-point of the line segment from P 1 ( x 1 , y 1 ) to P 2 ( x 2 , y 2 ) is x 1 + x 2 2 , y 1 + y 2 2 ### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805 ### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

#### Solutions

Chapter B, Problem 43E
To determine

## To calculate: To show that the mid-point of the line segment from P1(x1,y1) to P2(x2,y2) is x1+x22,y1+y22

Expert Solution

It is proved that themid-point of the line segment from P1(x1,y1) to P2(x2,y2) is x1+x22,y1+y22

### Explanation of Solution

Given information: Themid-point of the line segment from P1(x1,y1) to P2(x2,y2) is x1+x22,y1+y22

Formula Used:

According to Section formula, if the point (x,y) divides the line segment joining the points (x1,y1) and (x2,y2) in m:n , then

(x,y)=mx2+nx1m+n,my2+ny1m+n

Calculation:

Given two points P1(x1,y1) to P2(x2,y2)

Let us assume that (x,y) is the mid-point of the line segment joining the points P1 and P2

This means that point (x,y) divides the line segment joining the points P1 and P2 in a ratio 1:1

Here, m:n=1:1

Thus, using section formula, coordinates of point (x,y) is calculated as

(x,y)=mx2+nx1m+n,my2+ny1m+n

Substituting the values,

(x,y)=(1)x2+(1)x11+1,(1)y2+(1)y11+1(x,y)=x2+x11,y2+y12(x,y)=x1+x21,y1+y22

Conclusion:

Hence, proved thatthemid-point of the line segment from P1(x1,y1) to P2(x2,y2) is x1+x22,y1+y22

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