find point on the line in $R^n$ I am trying to find the coordinates of a middle point of a line in $\mathbb{R}^n$. Let $X(x_1, \ldots, x_n)$ and $Y=(y_1, \ldots, y_n)$ be two points in $\mathbb{R}^n$. How do I find the middle point $Z$ on the line $XY$? Thank you.

The midpoint of the segment from $a$ to $b$ on the real line is simply the arithmetic mean (ordinary average) of $a$ and $b$, $\frac12(a+b)$. The midpoint of the segment from $\langle a_1,a_2\rangle$ to $\langle b_1,b_2\rangle$ in the plane is $$\left\langle\frac{a_1+b_1}2,\frac{a_2+b_2}2\right\rangle\;,$$ found by averaging the coordinates; the proof is a simple argument involving similar triangles. Now generalize. You want the point that is midway between $X$ and $Y$ in **every** coordinate direction.