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Chapter 10: Q. 64 (page 791)

Prove that the midpoint of the line segment connecting the points x1,x2,鈥�,xn and y1,y2,鈥�,yn in鈩�n isx1+y12,x2+y22,鈥�,xn+yn2.

Short Answer

Expert verified

As a result, the coordinates of the line segment's midpoint Lis

x1+y12,x2+y22,鈰�,xn+yn2

Step by step solution

01

Introduction

Consider the following points inn-dimensional plane:

Px1,x2,鈥�,xnQy1,y2,鈥�,yn

Consider a line segment Ljoining the points P and $Q$.

The objective is to prove that the midpoint of the line segment $L$ is,

$$

\left(\frac{x_{1}+y_{1}}{2}, \frac{x_{2}+y_{2}}{2}, \ldots, \frac{x_{n}+y_{n}}{2}\right)

$$

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