Chapter 11.1, Problem 4ES

Suppose that a box has its faces paralled to the coordinate planes and the points $\left(x_1,y_1,z_1\right)\text{and}\left(x_2,y_2,z_2\right)$ are endpoints of a diagonal.

(a) Find the coordinates of the remaining six corners.

(b) Show that the midpoints of the line segment joining $\left(x_1,y_1,z_1\right)\text{and}\left(x_2,y_2,z_2\right)$ is

$\left(\frac{1}{2}\left(x_1+x_2\right),\frac{1}{2}\left(y_1+y_2\right),\frac{1}{2}\left(z_1+z_2\right)\right)$