Question

2 use the diagram to answer the following questions
a) how many points appear in the figure?
b) how many lines appear in the figure?
c) how many planes appear in the figure?
d) name three collinear points.
e) name four non - coplanar points.
f) give another name for line e.
g) name the intersection of (overrightarrow{pq}) and (overrightarrow{mn}).
h) name the intersection of plane (k) and line (e).
i) give another name for plane (l).
j) give another name for (overrightarrow{pq}).

Explanation:

Step1: Count points

By observing the figure, we count the distinct points. There are 9 points: $P, H, T, J, M, N, O, U, R$.

Step2: Count lines

Lines are straight - path connections between points. There are 2 lines: $\overleftrightarrow{PQ}$ and $\overleftrightarrow{MN}$.

Step3: Count planes

Planes are flat surfaces. There are 2 planes: plane $K$ and plane $L$.

Step4: Find collinear points

Collinear points lie on the same line. Points $M, N, O$ are collinear.

Step5: Find non - coplanar points

Non - coplanar points do not lie on the same plane. Points $P, H, M, O$ are non - coplanar.

Step6: Name line

Line $\overleftrightarrow{PQ}$ can be named as line $d$.

Step7: Find intersection of $\overrightarrow{PQ}$ and $\overrightarrow{MN}$

Since $\overrightarrow{PQ}$ and $\overrightarrow{MN}$ are skew lines (not in the same plane and do not intersect), there is no intersection point.

Step8: Find intersection of plane $K$ and line $c$

The intersection of plane $K$ and line $c$ is point $R$.

Step9: Rename plane $L$

Plane $L$ can be named as plane $JMN$.

Step10: Rename $\overrightarrow{PQ}$

$\overrightarrow{PQ}$ can be named as $\overrightarrow{PR}$.

Answer:

a) 9
b) 2
c) 2
d) $M, N, O$
e) $P, H, M, O$ (answers may vary)
f) line $d$
g) No intersection
h) $R$
i) plane $JMN$ (answers may vary)
j) $\overrightarrow{PR}$ (answers may vary)