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Prove that the midpoint of the line segment connecting the points x1,x2,,xn and y1,y2,,yn inn isx1+y12,x2+y22,,xn+yn2.

Short Answer

Expert verified

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

x1+y12,x2+y22,,xn+yn2

Step by step solution

01

Introduction

Consider the following points inn-dimensional plane:

Px1,x2,,xnQy1,y2,,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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