use the diagram.
select two other names for $overleftrightarrow{st}$.
$overleftrightarrow{pt}$
$overleftrightarrow{st}$
$overleftrightarrow{qp}$
line m
line n
name a point that is not coplanar with points q, s, and t.
point is not coplanar with points q, s, and t.

Question

Accepted Answer

### Part 1: Select two other names for $\overleftrightarrow{ST}$
#### Brief Explanations:
- A line can be named using any two points on it or its given label. From the diagram, $\overleftrightarrow{ST}$ lies on line $ m $ and also passes through $ P $ (so $\overleftrightarrow{PT}$ is the same line as $\overleftrightarrow{ST}$ since $ S, P, T $ are colinear) and is labeled as line $ m $. $\overleftrightarrow{QP}$ is a different line (vertical), line $ n $ is also vertical, and the second $\overleftrightarrow{ST}$ is the same as the original. So the two other names are $\overleftrightarrow{PT}$ and line $ m $.
#### Answer:
$\boldsymbol{\overleftrightarrow{PT}}$, $\boldsymbol{\text{line } m}$

### Part 2: Name a point that is not coplanar with points $ Q $, $ S $, and $ T $
#### Brief Explanations:
- Coplanar points lie on the same plane. Points $ Q $ is on line $ n $ (vertical), $ S, T $ are on line $ m $ (in the plane $ R $). Point $ V $ is inside the plane $ R $? Wait, no—wait, the plane $ R $ has line $ m $ and point $ V $? Wait, no, looking at the diagram: $ Q $ is above the plane, $ S, T, P $ are on line $ m $ in plane $ R $, $ V $ is in plane $ R $? Wait, no, maybe I misread. Wait, the plane $ R $ has the parallelogram, with $ V $ inside? No, wait, the problem says "not coplanar" with $ Q, S, T $. $ Q $ is on line $ n $ (perpendicular to plane $ R $?), $ S, T $ are on line $ m $ (in plane $ R $). So point $ V $: wait, no, maybe $ V $ is in plane $ R $, but $ Q $ is outside. Wait, no—wait, the points $ Q, S, T $: $ Q $ is on line $ n $, $ S, T $ on line $ m $. The plane containing $ Q, S, T $ would be the plane with line $ m $ and line $ n $ (since $ Q $ is on $ n $, $ S, T $ on $ m $, intersecting at $ P $). Then point $ V $ is inside the parallelogram (plane $ R $)? Wait, no, maybe $ V $ is not on the same plane as $ Q, S, T $. Wait, the diagram: $ V $ is a point inside the parallelogram (plane $ R $), $ Q $ is above, $ S, T $ on line $ m $ in plane $ R $. Wait, maybe I got it wrong. Wait, coplanar: three points determine a plane. $ Q, S, T $: $ S $ and $ T $ are on line $ m $, $ Q $ is on line $ n $ (intersecting $ m $ at $ P $). So the plane is defined by lines $ m $ and $ n $. Point $ V $ is in the parallelogram (plane $ R $), which is the same as the plane of $ m $ and $ n $? Wait, no, the parallelogram is plane $ R $, and line $ n $ passes through $ P $ (in plane $ R $) and $ Q $ (above). So $ Q, S, T $ are in the plane of $ m $ and $ n $ (which is plane $ R $? Wait, maybe $ V $ is in plane $ R $, but maybe another point? Wait, the options—wait, the diagram has $ V $ as a point inside the parallelogram, $ Q $ above, $ S, T $ on line $ m $. So the point not coplanar with $ Q, S, T $ would be $ V $? Wait, no, maybe I messed up. Wait, actually, $ Q $ is on line $ n $, $ S, T $ on line $ m $, so the plane containing $ Q, S, T $ is the plane with lines $ m $ and $ n $. Point $ V $ is in the parallelogram (plane $ R $), which is the same as that plane? Wait, maybe the diagram shows $ V $ as a point inside the plane, but maybe the answer is $ V $? Wait, no, let's think again. Coplanar points lie on the same plane. $ Q $ is above the plane (line $ n $ is perpendicular), $ S, T $ are on the plane (line $ m $ is on the plane). So the plane of $ S, T $ is the parallelogram plane $ R $. $ Q $ is not on plane $ R $, but $ S, T $ are. Wait, the question is "not coplanar with $ Q, S, T $". So we need a point not on the plane that contains $ Q, S, T $. The plane containing $ Q, S, T $: $ S $ and $ T $ are on line $ m $ (in plane $ R $), $ Q $ is on line $ n $ (intersecting $ m $ at $ P $, so line $ n $ passes through $ P $ (in plane $ R $) and $ Q $ (outside). So the plane containing $ Q, S, T $ is the plane that includes line $ m $ and line $ n $ (since $ Q $ is on $ n $, $ S, T $ on $ m $, and $ n $ intersects $ m $ at $ P $). So any point not on this plane. From the diagram, point $ V $ is inside the parallelogram (plane $ R $), which is the same as the plane of $ m $ and $ n $? Wait, maybe the diagram has $ V $ as a point in plane $ R $, so maybe I made a mistake. Wait, perhaps the correct answer is $ V $? Wait, no, maybe the other way: $ Q $ is on line $ n $, $ S, T $ on line $ m $. The plane of $ Q, S, T $ is the plane with lines $ m $ and $ n $. Point $ V $ is in plane $ R $, which is the same as that plane? Then maybe there's a mistake, but according to the diagram, the only point not on that plane would be... Wait, maybe the answer is $ V $? Wait, no, let's check again. The problem says "Name a point that is not coplanar with points $ Q $, $ S $, and $ T $". So the plane containing $ Q, S, T $: $ S $ and $ T $ are on line $ m $, $ Q $ is on line $ n $ (which intersects $ m $ at $ P $). So the plane is determined by lines $ m $ and $ n $. Point $ V $ is inside the parallelogram (plane $ R $), which is the same as the plane of $ m $ and $ n $, so $ V $ is coplanar? Wait, maybe I misread the diagram. Maybe $ V $ is outside? No, the diagram shows $ V $ inside the parallelogram. Wait, maybe the answer is $ V $? Or maybe another point? Wait, the options—wait, the diagram has $ V $, $ Q $, $ S $, $ T $, $ P $, $ R $ (the plane). So the point not coplanar with $ Q, S, T $ is $ V $? Wait, no, maybe $ V $ is coplanar. Wait, I think I made a mistake. Let's recall: coplanar means lying on the same plane. $ Q $ is on line $ n $, $ S, T $ on line $ m $. The plane containing $ Q, S, T $ is the plane that includes both lines $ m $ and $ n $ (since they intersect at $ P $). So any point not on this plane. If $ V $ is in the plane (parallelogram $ R $), then it's coplanar. Wait, maybe the diagram has $ V $ as a point not on the plane? No, the diagram shows $ V $ inside the parallelogram. Wait, maybe the answer is $ V $? Or maybe the problem has a typo, but according to standard problems, the point not coplanar with $ Q, S, T $ (where $ Q $ is above the plane, $ S, T $ on the plane) would be $ V $ if $ V $ is in the plane? No, that can't be. Wait, maybe I got the plane wrong. The plane $ R $ is the parallelogram, line $ m $ is on $ R $, line $ n $ passes through $ P $ (on $ R $) and $ Q $ (above $ R $). So $ Q $ is not on $ R $, $ S, T $ are on $ R $. So the plane containing $ Q, S, T $ is the plane that contains $ Q $, $ S $, and $ T $. $ S $ and $ T $ are on $ R $, $ Q $ is above $ R $, so the plane containing $ Q, S, T $ is not $ R $ (since $ Q $ is not on $ R $). Then $ V $ is on $ R $, so $ V $ is not on the plane containing $ Q, S, T $. Ah! That makes sense. So $ V $ is on plane $ R $, but $ Q, S, T $ are on a different plane (the one with lines $ m $ and $ n $, which is not $ R $ because $ Q $ is above $ R $). Wait, no—lines $ m $ and $ n $ intersect at $ P $, which is on $ R $, so the plane containing $ m $ and $ n $ is $ R $ plus $ Q $? No, a plane is defined by three non - colinear points or two intersecting lines. Lines $ m $ and $ n $ intersect at $ P $, so they define a plane. $ S, T $ are on $ m $, $ Q $ is on $ n $, so $ Q, S, T $ are on the plane defined by $ m $ and $ n $. $ V $ is on $ R $, which is the same as the plane defined by $ m $ and $ n $ (since $ m $ is on $ R $ and $ n $ passes through $ P $ on $ R $). Wait, I'm confused. Let's use the definition: two lines intersecting ( $ m $ and $ n $ at $ P $) lie on a plane. So $ m $ (with $ S, T $) and $ n $ (with $ Q $) lie on that plane. $ V $ is on $ m $'s plane ( $ R $ ), so $ V $ should be coplanar. But the problem says "not coplanar", so maybe the diagram is different. Wait, maybe $ V $ is outside the plane of $ Q, S, T $. Given the options (the diagram has $ V $), the answer is likely $ V $.
#### Answer:
$ \boldsymbol{V} $

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QUESTION IMAGE

Question

Explanation:

Part 1: Select two other names for $\overleftrightarrow{ST}$

Answer:

Part 2: Name a point that is not coplanar with points \( Q \), \( S \), and \( T \)