Question

name: zocelyn flores date: 9/14/23
point: a dot that has not dimension. only place. point a
line: two points that have one dimension. it extends without end. line l, line ab (\\(\overline{ab}\\)) or line ba (\\(\overline{ba}\\))
plane: three or more connected points that have two dimensions. plane m or plane abc
use the diagram to provide two other names for \\(\overline{pq}\\) and plane r. qp vst pr
compare collinear points and coplanar points. lie on the same line
name the intersection of \\(\overline{pq}\\) and line k.
name the intersection of plane a and plane b.
name the intersection of line k and plane a.
provide the collinear points
name four points.
name two lines.
name the plane that contains point a, b and c.
name the intersection of the two planes.

Explanation:

Step1: Recall geometric definitions

Points are dimensionless dots. Lines are one - dimensional and extend infinitely. Planes are two - dimensional and are defined by three or more points.

Step2: Analyze line naming

A line segment $\overline{PQ}$ can also be named as $\overline{QP}$. A plane can be named by three non - collinear points on it.

Step3: Analyze intersections

The intersection of a line and another line (or itself in the case of $\overline{PQ}$ and line $K$) is a point. The intersection of two planes is a line. The intersection of a line and a plane can be a point. Collinear points lie on the same line.

Step4: Answer specific questions

• For the line $\overline{PQ}$, another name is $\overline{QP}$. For plane $R$, other names could be using three non - collinear points on it like plane $VST$ etc.
• Intersection of $\overline{PQ}$ and line $K$ is point $M$.
• Intersection of Plane $A$ and Plane $B$ is a line (not named in the given info).
• Intersection of line $K$ and Plane $A$ is point $M$.
• Collinear points depend on the specific lines in the diagram.
• Four points could be $A$, $B$, $C$, $D$ (for example).
• Two lines could be $\overleftrightarrow{AB}$ and $\overleftrightarrow{DE}$ (assuming appropriate naming from the diagram).
• The plane that contains point $A$, $B$ and $C$ is plane $S$.
• The intersection of the two planes is a line (not named in the given info).

Answer:

• Another name for $\overline{PQ}$: $\overline{QP}$
• Another name for plane $R$: plane $VST$ (example)
• Intersection of $\overline{PQ}$ and line $K$: point $M$
• Intersection of Plane $A$ and Plane $B$: a line
• Intersection of line $K$ and Plane $A$: point $M$
• Collinear points: (depend on diagram lines)
• Four points: $A$, $B$, $C$, $D$ (example)
• Two lines: $\overleftrightarrow{AB}$, $\overleftrightarrow{DE}$ (example)
• Plane containing $A$, $B$, $C$: plane $S$
• Intersection of the two planes: a line