Question

1. 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 a line containing point v.
e) name the intersection of lines a and b.
f) give another name for line b.
g) name three non - collinear points.
h) give another name for plane d.

Explanation:

Step1: Count points

By observing the figure, we can see 5 distinct points: $V$, $W$, $X$, $Y$, $Z$.

Step2: Count lines

There are 2 lines: line $a$ (containing $V$ and $W$) and line $b$ (containing $Y$, $W$, $Z$).

Step3: Count planes

There is 1 plane labeled as $D$.

Step4: Name line with point $V$

Line $a$ (or $\overleftrightarrow{VW}$) contains point $V$.

Step5: Find intersection of lines

Lines $a$ and $b$ intersect at point $W$.

Step6: Rename line $b$

Line $b$ can also be named $\overleftrightarrow{ZY}$ as $Z$ and $Y$ are on it.

Step7: Find non - collinear points

$V$, $W$, $Z$ are non - collinear as they do not lie on the same straight line.

Step8: Rename plane

Another name for plane $D$ could be plane $VWXYZ$ (using the points on the plane).

Answer:

a) 5
b) 2
c) 1
d) $\overleftrightarrow{VW}$
e) $W$
f) $\overleftrightarrow{ZY}$
g) $V$, $W$, $Z$
h) plane $VWXYZ$