Lesson 1-1

Points, Lines & Planes

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1. 6x + 45 = 18 – 3x

2. x2 – 45 = 4

3. (3x + 4) + (4x – 7) = 11

4. (4x – 10) + (6x +30) = 180

5. Find the slope of the line k.

6. Find the slope of a perpendicular line to kStandardized Test Practice:

y

x

k

A

(0,1)

(-6,-2)

B

(6,4)C

A CB D1/2 2 -1/2 -2

5-Minute Check on Algebra5-Minute Check on Algebra5-Minute Check on Algebra5-Minute Check on Algebra Transparency 1-1

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

1. 6x + 45 = 18 – 3x

2. x2 – 45 = 4

3. (3x + 4) + (4x – 7) = 11

4. (4x – 10) + (6x +30) = 180

5. Find the slope of the line k.

6. Find the slope of a perpendicular line to kStandardized Test Practice:

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 1m = ----- = ----------- = -------- = ------ = ---- ∆x x2 – x1 6 – 0 6 2

A CB D1/2 2 -1/2 -2

y

x

k

A

(0,1)

(-6,-2)

B

(6,4)C

∆x∆y

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

Geometric Definitions

y

x

Coordinate Plane Examples

k

A (0,1)Point A or coordinates (0,1)Line kX,Y coordinate plane (intersection of x and y coordinate axes)

S

TR

D

E

F

Line RSLine Segments RT and STRays DE and DFAngle: EDFVertex: D (point)

Points R, P, and S are collinearPoints R, T, and S are not

P

y

x

k

A

(0,1)

(-6,-2)

B

(6,4)

C

Visual DefinitionsPoints

Line

Line Segments

Plane

A, B, C, D

k

BA, BC, AC

xy coordinate

D

(-5,5)

Collinear

Coplanar

A, B, C, D

A, B, C

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.

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 noncollinear points to name the plane.

plane JKM plane KLM plane JLM

Answer: line c,

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

Use the figure to name each of the following.

a. a line containing point X

b. a plane containing point Z

Answer: point

Answer: plane

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

Answer: line segment

a. How many planes appear in this figure?

Answer: two

b. Name three points that are collinear.

Sample answer: A, X, and Z

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