Question

refer to the figure.

1. name the lines that are only in plane q.
2. how many planes are labeled in the figure?
3. name the plane containing the lines m and t.
4. name the intersection of lines m and t.
5. name a point that is not coplanar with points a, b, and c.
6. are points f, m, g, and p coplanar? explain.
7. name the points not contained in a line shown.
8. what is another name for line t?
9. does line n intersect line q? explain.

Explanation:

Step1: Identify lines in plane Q

Lines $n$ and $q$ are only in plane $Q$.

Step2: Count labeled planes

There are 2 labeled planes, plane $Q$ and plane $R$.

Step3: Name plane with lines m and t

The plane containing lines $m$ and $t$ is plane $R$.

Step4: Find intersection of m and t

The intersection of lines $m$ and $t$ is point $C$.

Step5: Find non - coplanar point

Point $G$ is not coplanar with points $A$, $B$ and $C$ as $A$, $B$, $C$ are in plane $R$ and $G$ is in plane $Q$.

Step6: Check coplanarity of F, M, G, P

Points $F$, $M$, $G$, $P$ are not coplanar. Points $F$ is in plane $R$, $G$ and $P$ are in plane $Q$ and $M$ is on the line intersecting the two planes.

Step7: Name non - line points

Points $A$, $B$, $E$, $F$, $G$, $P$, $L$ are not contained in a line shown.

Step8: Rename line t

Another name for line $t$ is line $CE$.

Step9: Check intersection of n and q

Line $n$ does not intersect line $q$ as they are parallel lines in the same plane $Q$.

Answer:

1. Lines $n$ and $q$
2. 2
3. Plane $R$
4. Point $C$
5. Point $G$
6. No. Points $F$ is in plane $R$, $G$ and $P$ are in plane $Q$ and $M$ is on the line intersecting the two planes.
7. Points $A$, $B$, $E$, $F$, $G$, $P$, $L$
8. Line $CE$
9. No. They are parallel lines in the same plane $Q$.