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Lesson 1-1

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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
- 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.

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.

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

- 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

S

R

y

T

x

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)

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

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 noncollinearpoints to name the plane.

plane JKM plane KLM plane JLM

Answer: line c,

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

Answer: point

Answer: plane

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:
- 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