SL 3.1—3d space, volume, angles, midpoints

$\Delta x=7-3=4$, $\Delta y=4-(-2)=6$, $\Delta z=-1-5=-6$.

$d=\sqrt{4^2+6^2+(-6{)}^2}$.

$4^2=16$, $6^2=36$, $(-6{)}^2=36$, sum $=88$.

$d=\sqrt{88}$ units, the exact distance.

$\sqrt{28}$ comes from only using $\Delta x$ and $\Delta y$, forgetting the $z$-component entirely.

$\sqrt{52}$ results from squaring $\Delta z=-1-5=-6$ incorrectly as $\Delta z=-1+5=4$, giving $16+36+...$ mismatched, an arithmetic slip.

$\sqrt{112}$ arises from doubling one squared term by mistake, e.g. adding $36$ twice.

Only careful computation of all three squared differences gives $\sqrt{88}$, option A.

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

$M=\left(\frac{-4+2}{2},\frac{6+(-2)}{2},\frac{1+9}{2}\right)$.

$\frac{-2}{2}=-1$, $\frac{4}{2}=2$, $\frac{10}{2}=5$.

$M=(-1,2,5)$.

$(3,-4,4)$ comes from finding half the difference $\frac{x_2-x_1}{2}$ instead of the average, a swapped operation.

$(-1,4,10)$ results from adding instead of averaging the $y$ and $z$ coordinates.

$(6,-8,8)$ is simply the sum of coordinates without dividing by 2.

Averaging each coordinate correctly gives option A.