Identify the distance between the points $$ (9,7,3) $$ and $$ (5,3,2) $$ , and identify the midpoint of the segment for which these are the endpoints. Round to the nearest tenth, if necessary. $$ d \approx 5.7 $$ units; $$ M(2,2,0.5) $$ $$ d \approx 17.9 $$ units; $$ M(7,5,2.5) $$ $$ d \approx 5.7 $$ units; $$ M(7,5,2.5) $$ $$ d \approx 17.9 $$ units; $$ M(2,2,0.5) $$

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UpStudy AI · Accepted Answer

**Step 1. Compute the distance**

The distance $$ d $$ between two points $$(x_1, y_1, z_1)$$ and $$(x_2, y_2, z_2)$$ is given by:  
$$
d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}
$$

For the points $$(9,7,3)$$ and $$(5,3,2)$$:

- $$x$$-difference: $$9-5=4$$
- $$y$$-difference: $$7-3=4$$
- $$z$$-difference: $$3-2=1$$

Substitute into the formula:

$$
d = \sqrt{4^2 + 4^2 + 1^2} = \sqrt{16+16+1} = \sqrt{33} \approx 5.7
$$

**Step 2. Compute the midpoint**

The midpoint $$ M $$ is given by:

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

For the points $$(9,7,3)$$ and $$(5,3,2)$$:

$$
M = \left(\frac{9+5}{2}, \frac{7+3}{2}, \frac{3+2}{2}\right) = \left(\frac{14}{2}, \frac{10}{2}, \frac{5}{2}\right) = (7, 5, 2.5)
$$

**Final Answer**

$$
d \approx 5.7 \text{ units}; \quad M(7,5,2.5)
$$
The distance between the points is approximately 5.7 units, and the midpoint is at (7, 5, 2.5).

Identify the distance between the 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 the 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;