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 three collinear points.
e) name four non - coplanar points.
f) give another name for line e.
g) name the intersection of pq and mo.
h) name the intersection of plane k and line c.
i) give another name for plane l.
j) give another name for pq.

Explanation:

Step1: Count points

By observing the figure, we can count the points one - by - one. The points are P, Q, R, S, T, U, M, N, O. So there are 9 points.

Step2: Count lines

Identify the lines in the figure. The lines are PQ, MO, e, c, RN. So there are 5 lines.

Step3: Count planes

Locate the planes in the figure. The planes are K and L. So there are 2 planes.

Step4: Find collinear points

Collinear points lie on the same line. Points M, N, O are on line e, so three collinear points are M, N, O.

Step5: Find non - coplanar points

Non - coplanar points do not lie on the same plane. For example, points P, Q, R, T are non - coplanar (P is on plane K, Q on a line intersecting planes, R on a line outside plane K and T on plane K in a non - related position to the others).

Step6: Find intersection of PQ and MO

There is no intersection as they are skew lines (not in the same plane and do not intersect).

Step7: Find intersection of plane K and line c

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

Step8: Rename plane L

Plane L can also be named as plane MON (since three non - collinear points M, N, O lie on it).

Step9: Rename line PQ

Line PQ can also be named as line QP.

Answer:

a) 9 points
b) 5 lines
c) 2 planes
d) M, N, O
e) P, Q, R, T (answers may vary)
f) No intersection
g) Point R
h) Plane MON
i) Line QP