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### Lesson 1-1

Points, Lines & Planes

y

x

k

(6,4)

C

(0,1)

(-6,-2)

A

B

5-Minute Check on Algebra

- 6x + 45 = 18 – 3x
- x2 – 45 = 4
- (3x + 4) + (4x – 7) = 11
- (4x –10) + (6x +30) = 180
- Find the slope of the line k.
- Find the slope of a perpendicular line to k

Standardized Test Practice:

A

B

C

D

-2

1/2

2

-1/2

Click the mouse button or press the Space Bar to display the answers.

y

x

k

(6,4)

C

(0,1)

(-6,-2)

A

B

5-Minute Check on Algebra

- 6x + 45 = 18 – 3x
- x2 – 45 = 4
- (3x + 4) + (4x – 7) = 11
- (4x –10) + (6x +30) = 180
- Find the slope of the line k.
- Find the slope of a perpendicular line to k

9x +45 = 18 9x = -27 x = -3

x² = 49 x = √49 x = +/- 7

7x - 3 = 11 7x = 14 x = 2

10x + 20 = 180 10x = 160 x = 16

∆y y2 – y1 4 – 1 3 1

m = ----- = ----------- = -------- = ------ = ----

∆x x2 – x1 6 – 0 6 2

∆y

∆x

Standardized Test Practice:

A

B

C

D

-2

1/2

2

-1/2

Click the mouse button or press the Space Bar to display the answers.

Objectives

- Identify and model points, lines and planes
- Identify collinear and coplanar points and intersecting lines and planes in space

Vocabulary

- Point – a location in space; usually named by coordinate location (x,y)
- Line segment – a collection of collinear points between two points
- Line – a collection of points, defined by two points
- Collinear – points on the same line are called collinear
- Plane – flat surface made up of points; defined by at least three points (or two intersecting lines)
- Coplanar – points lying on the same plane are called coplanar
- Space – is a boundless, three dimensional set of all points

R

y

T

x

Geometric DefinitionsE

Line RS

Line Segments RT and ST

Rays DE and DF

Angle: EDF

Vertex: D (point)

Points R, P, and S are collinear

Points R, T, and S are not

F

D

P

Coordinate Plane Examples

k

Point A or coordinates (0,1)

Line k

X,Y coordinate plane (intersection of x and y coordinate axes)

A

(0,1)

Visual Definitions

Points

y

A, B, C, D

k

Line

(-5,5)

k

(6,4)

D

C

Collinear

(0,1)

A, B, C

x

A

Line Segments

(-6,-2)

B

BA, BC, AC

Plane

xy coordinate

Coplanar

A, B, C, D

Example 1-1a

Use the figure to name a line containing point K.

Answer: The line can be named as line a.

There are three points on the line. Any two of the points can be used to name the line.

Example 1-1b

Use the figure to name a plane containing point L.

Answer: The plane can be named as plane B.

You can also use the letters of any three noncollinearpoints to name the plane.

plane JKM plane KLM plane JLM

Example 1-1d

Use the figure to name each of the following.

a. a line containing point X

b. a plane containing point Z

Answer: plane P, plane XYZ, plane ZYX, plane YZX, plane XZY, plane ZXY, plane YXZ

VISUALIZATION Name the geometric shape modeled by each object.

a. a colored dot on a map used to mark the location of a city

b. the ceiling of your classroom

c. the railing on a stairway

Example 1-2dAnswer: point

Answer: plane

Answer: line segment

Example 1-4g

c. Are points X, O, and R coplanar? Explain.

Answer: Points X, O, and R all lie in plane T, so they are coplanar.

Summary & Homework

- Summary:
- Two points determine a line
- Three noncollinear points determine a plane
- Homework:
- pg 9,10: 7-8, 13, 15, 17, 22-23, 32, 34-35

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