Question

NO LINKS!!! Please assist me​

Answer 1

Answer:

$\textsf{a.} \quad \overleftrightarrow{AV} \; \textsf{and} \; \overleftrightarrow{RV}$

$\textsf{b.} \quad STZ, \; RTZ, \;QTZ$

$\textsf{c.} \quad A, R\; \textsf{and}\; V$

$\textsf{d.} \quad Q,S,T \; \textsf{and}\; Z$

$\textsf{e.} \quad \overline{AR}$

$\textsf{f.} \quad \overrightarrow{RA} \; \textsf{and} \; \overrightarrow{RV}$

Step-by-step explanation:

Part a

A line can be named by using two points on the line or by a (lowercase) letter.

Therefore, two other names for line p are:

• $\overleftrightarrow{AV}$
• $\overleftrightarrow{RV}$

Part b

A plane can be named by using three non-collinear points in the plane or by a (capital script) letter.

Therefore, three other names for plane W are:

• STZ
• RTZ
• QTZ

Part c

Collinear points are points that lie on the same line.

The collinear points on the given diagram are: A, R & V, and S, R & Q.

Therefore, three points that are collinear are:

• A, R and V

Part d

Coplanar points are three or more points that lie in the same plane.

The coplanar points on the given diagram are: Q, R, S, T and Z

Therefore, four points that are coplanar are:

• Q, S, T and Z

Part e

A line segment is part of a line that has two endpoints, and is named by its two endpoints.

The line segments on the given diagram are:

$\overline{AR}, \;\overline{RV}, \; \overline{AV}, \; \overline{SR}, \; \overline{RQ} \; \textsf{and}\; \overline{SQ}.$

Therefore, a line segment is:

• $\overline{AR}$

Part f

A ray is a part of a line that has one endpoint (so continues infinitely in the direction without an endpoint).  

Opposite rays are two rays that have a common endpoint and form a line.  They are named by the common endpoint followed by any other point on each ray.

The pairs of opposite rays on the given diagram are:

$\overrightarrow{RA} \; \textsf{and} \; \overrightarrow{RV}, \quad \overrightarrow{RS} \; \textsf{and} \; \overrightarrow{RQ}$

Therefore, a pair of opposite rays are:

• $\overrightarrow{RA} \; \textsf{and} \; \overrightarrow{RV}$

Answer 2

Answers in bold:

• (a)  Line AV and line RV
• (b)  Plane SRZ, plane TRS, plane QTZ
• (c)  Points S, R and Q
• (d)  Points Q, T, R, and S
• (e)  Line segment RV
• (f)   Ray RA and ray RV

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Explanation:

Part (a)

Pick any two points on line p. I'll go for points A and V. They lead to the name "line AV". The order doesn't matter so we could say "line VA"

Or you could pick points A and R to get line AR, and so on.

There are 6 different ways to name this line. We found 2 so far, and I'll let you find the other four.

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Part (b)

To name a plane, we need 3 points that reside in it. Points R, S and Z are in the vertical plane W. So we could call it "Plane SRZ". The order of the points doesn't matter.

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Part (c)

The term "collinear" means the points are on the same straight line. This applies to points S, R and Q. Also, it applies to points A, R, and V.

We cannot say something like "points S, R, and V are collinear" since they are on different lines. The points need to be on the same straight line.

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Part (d)

Coplanar points are part of the same plane. Pick your four favorite points in plane W that is shaded. You cannot select W since it's not a point.

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Part (e)

A line segment has a fixed length. Neither endpoint goes on forever. Technically there aren't any segments shown on this diagram since we have lines only. Though if we focus on a subset of say line AV, then segment RV is one possible line segment.

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Part (f)

Like with part (e), there are technically only lines here and nothing else. But we could break the line apart to get 2 rays.

A ray has one fixed endpoint and it points forever in one direction only. Think of a ray of light. An example of a ray is to start at point R and go forever toward point V. This forms ray RV. A similar situation happens with ray RA.

The order is important. The notation Ray RV is different from Ray VR since the first letter tells us the fixed endpoint that doesn't go on forever.

Notice how rays RV and RA, when joined together, form a straight line. They point in opposite directions. You could think of it like one is pointing north and the other points south.