pre-algebra 5-5 coordinate geometry 5-5 coordinate geometry pre-algebra warm up warm up problem of...

Pre-Algebra

5-5 Coordinate Geometry5-5 Coordinate Geometry

Pre-Algebra

Warm Up

Problem of the Day

Lesson Presentation

Pre-Algebra

5-5 Coordinate Geometry

Warm UpComplete each sentence.

1. Two lines in a plane that never meet are called lines.

2. lines intersect at right angles.

3. The symbol || means that lines are .4. When a transversal intersects two lines, all of the acute angles are congruent.

parallel

Perpendicular

parallel

Pre-Algebra


parallel

Pre-Algebra


Problem of the Day

What type of polygon am I? My opposite angles have equal measure. I do not have a right angle. All my sides are congruent. rhombus

Pre-Algebra


Learning Goal Assignment

Learn to identify polygons in the coordinate plane.

Pre-Algebra


Vocabularyslope

rise

run

Pre-Algebra


In computer graphics, a coordinate system is used to create images, from simple geometric figures to realistic figures used in movies.

Properties of the coordinate plane can be used to find information about figures in the plane, such as whether lines in the plane are parallel.

Pre-Algebra


Slope is a number that describes how steep a line is.

Pre-Algebra


The slope of a horizontal line is 0. The slope of a vertical line is undefined.

slope =vertical change

horizontal change= rise

run

Pre-Algebra


Additional Example 1A: Finding the Slope of a Line

Determine if the slope of each line is positive, negative, 0, or undefined. Then find the slope of each line.

A. XY

positive slope;

slope of XY = = –5–4

54

Pre-Algebra



B. ZA

negative slope;

slope of ZA = = ––1 2

12

Additional Example 1B: Finding the Slope of a Line

Pre-Algebra



C. BC

slope of BC is undefined

Additional Example 1C: Finding the Slope of a Line

Pre-Algebra



D. DM

slope of DM = 0

Additional Example 1D: Finding the Slope of a Line

Pre-Algebra


Try This: Example 1A


A. AB A

C

B

D

FE

HG

positive slope;

slope of AB = 1 8

Pre-Algebra


B. CD

slope of CD is undefined

Try This: Example 1B


A

C

B

D

FE

HG

Pre-Algebra


C. EF

slope of EF = 0

Try This: Example 1C


A

C

B

D

FE

HG

Pre-Algebra


D. GH

Try This: Example 1D


A

C

B

D

FE

HG

negative slope;

slope of GH = = ––1 3

13

Pre-Algebra


Slopes of Parallel and Perpendicular Lines

Two lines with equal slopes are parallel.

Two lines whose slopes have a product of –1 are perpendicular.

Pre-Algebra


Additional Example 2: Finding Perpendicular Line and Parallel Lines

Which lines are parallel? Which lines are perpendicular?

slope of EF = 32

slope of GH = 35

slope of PQ = 35

slope of QR = or –1 3 –3

2 3

slope of CD = or – –2 3

Pre-Algebra


Additional Example 2 Continued

The slopes are equal. =35

35

The slopes have a product

of –1: • – = –132

2 3

GH || PQ

EF CD


Pre-Algebra


Try This: Example 2

A

C

B

D

F

E

K

JH

G


slope of AB = or –6 4

–3 2

slope of CD = –2 3

slope of EF = or –4 6

–2 3

slope of GH = 23

slope of JK = or 1 3 3

Pre-Algebra


CD || EF

GH AB

A

C

B

D

F

E

K

JH

G

Try This: Example 2 Continued


The slopes are equal. =–2 3

–2 3

The slopes have a product

of –1: • – = –123

3 2

Pre-Algebra


Lesson Quiz

Determine the slope of each line.

1. PQ

2. MN

3. MQ

4. NP

5. Which pair of lines are parallel?

1

8

7

– 10 3

MN, RQ

pre-algebra 5-5 coordinate geometry 5-5 coordinate geometry pre-algebra warm up warm up problem of...

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