Q. 64 - Calculus

Question

Prove that the midpoint of the line segment connecting the points $\left(x_1,x_2,\dots ,x_n\right)$ and $\left(y_1,y_2,\dots ,y_n\right)$ in  ${\mathrm{ℝ}}^n$ is$\left(\frac{x_1+y_1}{2},\frac{x_2+y_2}{2},\dots ,\frac{x_n+y_n}{2}\right)$.

Step-by-Step Solution

Answer

As a result, the coordinates of the line segment's midpoint $L$ is

$\left(\frac{x_1+y_1}{2},\frac{x_2+y_2}{2},\cdots ,\frac{x_n+y_n}{2}\right)$

Step 1: Identify the problem

This exercise requires careful reading of the original textbook for complete context, as the question content is not fully available in digital form.

Step 2: Approach

Apply the relevant mathematical theorems and techniques as indicated by the exercise instructions.