Question

part ii: short answer
use the diagram to the right for questions 1 - 4:

1. name two points collinear to point d.
2. give another name for line p.
3. name the intersection of line r and plane k.
4. name a point non - coplanar to plane k.

use the diagram to the right for questions 5 - 8:

1. how many planes appear in the figure?
2. name four coplanar points.
3. name a point non - coplanar to plane z.
4. name the intersection of plane jps and plane z.

use the diagram to the right for questions 9 - 12:

1. name two planes:
2. provide 2 lines that are skew to line qp:
3. assuming there is a right angle at each vertex s, what two lines are perpendicular?
4. name two lines parallel to line xw.

Explanation:

Step1: Recall collinear points definition

Collinear points lie on the same line. In the first - diagram, points on the same line as D are A and E.

Step2: Recall line naming convention

A line can be named by any two points on it. Line p can be named as line AE.

Step3: Find intersection of line and plane

The intersection of line r and plane K is point Y.

Step4: Identify non - coplanar point

A non - coplanar point to plane K is W.

Step5: Count planes in the second diagram

The planes in the second diagram are plane Z, plane JPS, plane PMLK, plane SRML, plane PQRS, plane JKLM. So there are 6 planes.

Step6: Name coplanar points

In the second diagram, points J, K, L, M are coplanar (lying on plane Z).

Step7: Name non - coplanar point to plane Z

Point P is non - coplanar to plane Z.

Step8: Find intersection of two planes

The intersection of plane JPS and plane Z is line JK.

Step9: Name planes in the third diagram

Two planes in the third diagram are plane PQRS and plane WXYZ.

Step10: Identify skew lines

Skew lines are non - parallel and non - intersecting. Lines JR and WZ are skew to line QP.

Step11: Find perpendicular lines

Assuming right angles at vertices, lines QP and PZ are perpendicular.

Step12: Find parallel lines

Lines SR and YZ are parallel to line XW.

Answer:

1. A, E
2. Line AE
3. Y
4. W
5. 6
6. J, K, L, M
7. P
8. Line JK
9. Plane PQRS, Plane WXYZ
10. JR, WZ
11. QP, PZ
12. SR, YZ