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Lesson 1-1. Point, Line, Plane. Points. Points do not have actual size. How to Sketch: Using dots How to label: Use capital letters Never name two points with the same letter (in the same sketch). . A. B. A. C. Lines.

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lesson 1 1

Lesson 1-1

Point, Line, Plane

Lesson 1-1 Point, Line, Plane

points
Points
  • Points do not have actual size.
  • How to Sketch:

Using dots

  • How to label:

Use capital letters

Never name two points with the same letter

(in the same sketch).

A

B

A

C

Lesson 1-1 Point, Line, Plane

lines
Lines
  • Lines extend indefinitely and have no thickness or width.
  • How to sketch : using arrows at both ends.
  • How to name: 2 ways

(1) small script letter – line n

(2) any two points on the line -

  • Never name a line using three points -

n

A

B

C

Lesson 1-1 Point, Line, Plane

collinear points
Collinear Points
  • Collinear points are points that lie on the same line. (The line does not have to be visible.)
  • A point lies on the line if the coordinates of the point satisfy the equation of the line.

Ex: To find if A (1, 0) is collinear with

the points on the line y = -3x + 3.

Substitute x = 1 and y = 0 in the equation.

0 = -3 (1) + 3

0 = -3 + 3

0 = 0

The point A satisfies the equation, therefore the point is collinear

with the points on the line.

A

B

C

Collinear

C

A

B

Non collinear

Lesson 1-1 Point, Line, Plane

planes
Planes
  • A plane is a flat surface that extends indefinitely in all directions.
  • How to sketch: Use a parallelogram (four sided figure)
  • How to name: 2 ways

(1) Capital script letter – Plane M

(2) Any 3 non collinear points in the plane - Plane: ABC/ ACB / BAC / BCA / CAB / CBA

A

M

B

C

Horizontal Plane

Vertical Plane

Other

Lesson 1-1 Point, Line, Plane

different planes in a figure
Different planes in a figure:

A

B

Plane ABCD

Plane EFGH

Plane BCGF

Plane ADHE

Plane ABFE

Plane CDHG

Etc.

D

C

E

F

H

G

Lesson 1-1 Point, Line, Plane

other planes in the same figure
Other planes in the same figure:

Any three non collinear points determine a plane!

Plane AFGD

Plane ACGE

Plane ACH

Plane AGF

Plane BDG

Etc.

Lesson 1-1 Point, Line, Plane

coplanar objects
Coplanar Objects

Coplanar objects (points, lines, etc.) are objects that lie on the same plane. The plane does not have to be visible.

Are the following points coplanar?

A, B, C ?

Yes

A, B, C, F ?

No

H, G, F, E ?

Yes

E, H, C, B ?

Yes

A, G, F ?

Yes

C, B, F, H ?

No

Lesson 1-1 Point, Line, Plane

intersection of figures
Intersection of Figures

The intersection of two figures is the set of points that are common in both figures.

The intersection of two lines is a point.

m

Line m and line n intersect at point P.

P

n

Continued…….

Lesson 1-1 Point, Line, Plane

3 possibilities of intersection of a line and a plane
3 Possibilities of Intersection of a Line and a Plane

(1) Line passes through plane – intersection is a point.

(2) Line lies on the plane - intersection is a line.

(3) Line is parallel to the plane - no common points.

Lesson 1-1 Point, Line, Plane

intersection of two planes is a line
Intersection of Two Planes is a Line.

B

P

A

R

Plane P and Plane R intersect at the line

Lesson 1-1 Point, Line, Plane