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Lesson 1-1. Points, Lines & Planes. Transparency 1-1. y. x. k. (6,4). C. (0,1). (-6,-2). A. B. 5-Minute Check on Algebra. 6x + 45 = 18 – 3x x 2 – 45 = 4 (3x + 4) + (4x – 7) = 11 (4x – 10) + (6x +30) = 180 Find the slope of the line k.

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Lesson 1-1

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Lesson 1 1

Lesson 1-1

Points, Lines & Planes


Lesson 1 1

Transparency 1-1

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.


Lesson 1 1

Transparency 1-1

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

Objectives

  • Identify and model points, lines and planes

  • Identify collinear and coplanar points and intersecting lines and planes in space


Vocabulary

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


Geometric definitions

S

R

y

T

x

Geometric Definitions

E

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

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

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

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

Answer: line c,

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


Example 1 2d

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 1-2d

Answer: point

Answer: plane

Answer: line segment


Example 1 4e

Example 1-4e

a. How many planes appear in this figure?

Answer: two


Example 1 4f

Example 1-4f

b. Name three points that are collinear.

Sample answer:A, X, and Z


Example 1 4g

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 & 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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