The coordinates of the midpoints of the line segment joining the points (2, 3, 4) and (8, -3, 8) are

The correct option is (5, 0, 6).

To find the coordinates of the midpoint of the line segment joining two points in three-dimensional space, we use the midpoint formula.
If we have two points, $P_1(x_1,y_1,z_1)$ and $P_2(x_2,y_2,z_2)$, the coordinates of the midpoint $M(x,y,z)$ are given by the formula:

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

Given the points:
$(x_1,y_1,z_1)=(2,3,4)$
$(x_2,y_2,z_2)=(8,-3,8)$

Now, we calculate each coordinate of the midpoint step-by-step:

For the x-coordinate:
$x=\frac{2+8}{2}=\frac{10}{2}=5$

For the y-coordinate:
$y=\frac{3+(-3)}{2}=\frac{0}{2}=0$

For the z-coordinate:
$z=\frac{4+8}{2}=\frac{12}{2}=6$

Combining these values, we find that the coordinates of the midpoint are $(5,0,6)$.