Identify the distance between points $$ (-1,7,10) $$ and $$ (6,-3,2) $$, and identify the midpoint of the segment for which these are the endpoints. Round to the nearest tenth, if necessary. $$ d \approx 6 $$ units; $$ M(3.5,1,6.5) $$ $$ d \approx 14.6 $$ units; $$ M(3.5,1,6.5) $$ $$ d \approx 6 $$ units; $$ M(2.5,2,6) $$ $$ d \approx 14.6 $$ units; $$ M(2.5,2,6) $$

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We begin by finding the distance between the points $$(-1,7,10)$$ and $$(6,-3,2)$$. The distance formula in 3-dimensional space is given by

$$
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2}.
$$

Substitute the coordinates:

$$
d = \sqrt{(6 - (-1))^2 + (-3 - 7)^2 + (2 - 10)^2}.
$$

Calculate each difference:

$$
6 - (-1) = 7,\quad -3 - 7 = -10,\quad 2 - 10 = -8.
$$

Square these differences:

$$
7^2 = 49,\quad (-10)^2 = 100,\quad (-8)^2 = 64.
$$

Sum the squares:

$$
49 + 100 + 64 = 213.
$$

Thus, the distance is

$$
d = \sqrt{213} \approx 14.6 \text{ units}.
$$

Next, we find the midpoint $$ M $$ of the segment connecting the points. The midpoint formula in 3-dimensional space is

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

Substitute the coordinates:

$$
M = \left( \frac{-1 + 6}{2},\, \frac{7 + (-3)}{2},\, \frac{10 + 2}{2} \right).
$$

Calculate each component:

$$
\frac{-1 + 6}{2} = \frac{5}{2} = 2.5,\quad \frac{7 - 3}{2} = \frac{4}{2} = 2,\quad \frac{10 + 2}{2} = \frac{12}{2} = 6.
$$

Thus, the midpoint is

$$
M(2.5,\, 2,\, 6).
$$

The correct answer is:

$$
d \approx 14.6 \text{ units}; \quad M(2.5,\, 2,\, 6).
$$
The distance between the points is approximately 14.6 units, and the midpoint is at (2.5, 2, 6).

Identify the distance between points and
, and identify the midpoint of the segment for which
these are the endpoints. Round to the nearest tenth, if
necessary.
units;
units;
units;
units;

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Identify the distance between points and , and identify the midpoint of the segment for which these are the endpoints. Round to the nearest tenth, if necessary. units; units; units; units;