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1.1Points,Lines,andPlanesMTIII.notebook
1
August 24, 2015
Aug 248:31 AM
Points, Lines, and Planes
Jul 189:25 AM
Coordinate Geometryexample: battleship
ordered paır(x, y)
coordınateplane
ıı
ııı
Warm-Up/Review
1.1Points,Lines,andPlanesMTIII.notebook
2
August 24, 2015
Aug 193:01 PM
Plotting Practice
Aug 52:18 PM
(5,8)
x
y
(3,2)
A B
C
D
Find the unknown coordinates:
1.1Points,Lines,andPlanesMTIII.notebook
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August 24, 2015
Aug 810:18 AM
Points, Lines, & Planes
explaıned only by examples and pıctures
Aug 135:03 PM
poınt• sımplest fıgure- no sıze• named by capıtal letter p• represents a locatıon or ordered paır
Example
p(2,4)
1.1Points,Lines,andPlanesMTIII.notebook
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May 3012:18 PM
the set of allpoınts
space
Jul 199:34 AM
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
1.1Points,Lines,andPlanesMTIII.notebook
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August 24, 2015
Jul 1910:14 AM
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
Aug 810:19 AM
1.1Points,Lines,andPlanesMTIII.notebook
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August 24, 2015
Aug 263:27 PM
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.
Aug 810:22 AM
1.1Points,Lines,andPlanesMTIII.notebook
7
August 24, 2015
Aug 811:04 AM
Aug 810:28 AM
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:
1.1Points,Lines,andPlanesMTIII.notebook
8
August 24, 2015
Jul 189:47 AM
(0,2) (1, 5) (-1,-1) y = 3x + 2
Are these points collinear?
(2,3) (1, 2) (-1,-2) y = x + 4
Example 3:
Jul 189:49 AM
a.) Find 3 pts on y = -3x +3b.) Graph the linec.) Name one point not on the line
Example 4:
a.) b.) c.) check
1.1Points,Lines,andPlanesMTIII.notebook
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August 24, 2015
Jul 1910:34 AM
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:
Aug 263:34 PM
*collinear
*noncollinear
*coplanar
*noncoplanar
Find 3 points that are:
1.1Points,Lines,andPlanesMTIII.notebook
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August 24, 2015
May 3010:17 AM
has two poınts called endpoınts
lıne segment
wrıtten as: ab or l
A
B
l
Aug 263:37 PM
raybegıns at a poınt andcontınues ındefınıtely
wrıtten as: ab
AB
1.1Points,Lines,andPlanesMTIII.notebook
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Aug 810:32 AM
Aug 263:46 PM
• point• segment• plane• collinear pts• coplanar pts
Using these pictures,identify thefollowingfor each
1.1Points,Lines,andPlanesMTIII.notebook
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Aug 810:35 AM
Example 6:
Aug 810:44 AM
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
1.1Points,Lines,andPlanesMTIII.notebook
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Aug 811:08 AM
Example 7:
Oct 23:22 PM
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...
1.1Points,Lines,andPlanesMTIII.notebook
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August 24, 2015
Aug 263:50 PM
name each of the followıng lınes ın 2 dıfferent ways.
1.
2.
3.
M A
AB
C
PMl