1.1: The Coordinate Plane- Points Lines and Planes

M(G&M)–10–9 Solves problems on and off the coordinate plane involving distance, midpoint, perpendicular and parallel lines, or slope

GSE

Quadrants

Origin- where the x and y axis meet

(0,0)

(+,+)(-, +)

(-,-) (+,-)

Ex.

Graph the points:

A ( 2,3)

B (-1,2)

C( -3, -3)

D (0, -2)

A

B

C

D

Ex.

• Find the missing Coordinates

A(5,2)

B( , ) C ( -3, -4)

D ( )

5 -4

-3 , 2

Ex 2.

R ( )

S ( 6 , -8 )P ( )

W ( -4 , 7 )6 , 7

-4 , -8

PointPoint

1. Has no dimension (no length, width, 1. Has no dimension (no length, width, thickness)thickness)

2. Usually represented by a dot2. Usually represented by a dot

3. Named using one capital letter3. Named using one capital letter

• BB

LineLine1.1. Extends forever in one dimension (length)Extends forever in one dimension (length)

2.2. Has an arrowhead on each end Has an arrowhead on each end representing the fact that it goes on representing the fact that it goes on foreverforever

3.3. Consists of an infinite amount of pointsConsists of an infinite amount of points

4.4. Always straightAlways straight

5.5. Named with a lowercase script letter or by Named with a lowercase script letter or by 2 points on the line2 points on the line

AA BB

ll

Can be called:Can be called:

Line Line ll

Line AB or ABLine AB or AB

Line BA or BALine BA or BA

Example of a line

• Name the line AD as many ways possible

DefinitionsDefinitions

• Coplanar pointsCoplanar points – –

• Collinear Points –

Points that lie on the same line

points that lie on the same points that lie on the same planeplane

PlanePlane

1.1. Extends forever in 2 dimensions (length & Extends forever in 2 dimensions (length & width)width)

2.2. Usually represented by a 4-sided figureUsually represented by a 4-sided figure

3.3. Named with a capital script letter or 3 non-Named with a capital script letter or 3 non-collinear points on the surface of the planecollinear points on the surface of the plane

AA

BC

W Can be named:Can be named:

1)Plane 1)Plane WW

oror

2)Plane ABC, plane BCA, plane CBA, 2)Plane ABC, plane BCA, plane CBA, etc.etc.

When 2 planes intersect, their When 2 planes intersect, their intersection is a …intersection is a …

Line

• Name the intersection of Plane P and

Plane R• Line AB or BH

When a line intersects a plane, their intersection is a …

Point

Name the intersection of line m with the plane K

Line SegmentLine Segment (or segment) (or segment)

• A section of a line that has 2 endpointsA section of a line that has 2 endpoints

• Named by its endpoints. AB or BANamed by its endpoints. AB or BA• Order doesn’t matter with segmentsOrder doesn’t matter with segments

AA BB

How many line segmentsmake up this graph?

Name Them

G

A

B

T

Problems to complete