1.1­Points,Lines,andPlanes­MTIII.notebook

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Points, Lines, and Planes

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Coordinate Geometryexample: battleship

ordered paır(x, y)

coordınateplane

ıı

ııı

Warm-Up/Review

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Plotting Practice

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(5,8)

x

y

(­3,­2)

A B

C

D

Find the unknown coordinates:

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 Points, Lines, & Planes

explaıned only by examples and pıctures

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poınt• sımplest fıgure- no sıze• named by capıtal letter p• represents a locatıon or ordered paır

Example

p(2,4)

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the set of allpoınts

space

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lıne• segments connectıng 2 poınts and extendıng ındefınıtely ın both dırectıons• named by lower case scrıpt letter or lıne ab or ab

m

AB

Examples

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plane• flat surface- no thıckness• extends ınfınıtely ın all dırectıons• named by capıtal scrıpt letter or 3 noncollınear poınts ın a plane

RP Q

R

Plane PQR

Examples

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Ex.

The prefix "co" means TOGETHER

colınear poınts are on the same lıne

coplanarpoınts are on the same plane*lınes can also be coplanar*

Ex.

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Refer to the design in the roof of Beijing's National Stadium.

1.  Name four coplanar points.

2.  Name three lines.

3.  Name two planes.

Example 2:

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(0,2) (1, 5) (-1,-1) y = 3x + 2

Are these points collinear?

(2,3) (1, 2) (-1,-2) y = x + 4

Example 3:

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a.) Find 3 pts on y = -3x +3b.) Graph the linec.) Name one point not on the line

Example 4:

a.) b.) c.) check

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a.) are the poınts s,t,u collınear? b.) are the poınts r,s,t coplanar?c.) use 3 poınts to defıne a plane other than plane m.

m

u

tr

s

Example 5:

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*collinear

*noncollinear

*coplanar

*noncoplanar

Find 3 points that are:

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has two poınts called endpoınts

lıne segment

wrıtten as: ab or l

A

B

l

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raybegıns at a poınt andcontınues ındefınıtely

wrıtten as: ab

AB

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• point• segment• plane• collinear pts• coplanar pts

Using these pictures,identify thefollowingfor each

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Example 6:

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IntersectionsTwo or more geometric figures intersect if they have one or more points in common.  The intersection of the figures is the set of points the figures have in common.  

m

n

A

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Example 7:

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Through any 2 points, there is exactly one line. BA

Through any 3 points not on the same line, there is exactly one plane.A plane contains at least 3 points not on the same line.

If two points lie in a plane, then the entire line containing those 2 points lie in that plane.

If 2 planes intersect, then their intersection is a line.

A

C

B

AB

POSTULATES to know...

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name each of the followıng lınes ın 2 dıfferent ways.

1.

2.

3.

M A

AB

C

PMl

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