pre-algebra 5.5 coordinate geometry. complete each sentence. 1. two lines in a plane that never meet...

Pre-Algebra

5.5

Coordinate Geometry

Complete 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

parallelparallel

Warm Up

Learn to identify polygons in the coordinate plane.

slope

rise

run

Vocabulary

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

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

slope =vertical change

horizontal change= rise

run

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

Example: Finding the Slope of a Line


B. ZA

negative slope;

slope of ZA = = ––1 2

12



C. BC

slope of BC is undefined



D. DM

slope of DM = 0



A. AB A

C

B

D

FE

HG

positive slope;

slope of AB = 1 8

Try This

B. CD

slope of CD is undefined


A

C

B

D

FE

HG

Try This

C. EF

slope of EF = 0


A

C

B

D

FE

HG

Try This

D. GH


A

C

B

D

FE

HG

negative slope;

slope of GH = = ––1 3

13

Try This

Slopes of Parallel and Perpendicular Lines

Two lines with equal slopes are parallel.

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

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

Example: Finding Perpendicular Line and Parallel Lines

The slopes are equal. =35

35

The slopes have a product

of –1: • – = –132

2 3

GH || PQ

EF CD


Example Continued

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

Try This

CD || EF

GH AB

A

C

B

D

F

E

K

JH

G


The slopes are equal. =–2 3

–2 3

The slopes have a product

of –1: • – = –123

3 2

Try This

Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral.A. A(3, –2), B(2, –1), C(4, 3), D(5, 2)

parallelogram

CD || BA and BC || AD

Example: Using Coordinates to Classify Quadrilaterals

B. R(–3, 1), S(–4, 2), T(–3, 3), U(–2, 2)

parallelogram, rectangle, rhombus, square

Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral.

TU || SR and ST || RU

TURU, RURS, RSST and STTU


C. G(1, –1), H(1, –2), I(3, –3), J(3, 1)

trapezoid


GH || JI


D. W(2, –3), X(3, –4), Y(6, –1), Z(5, 0)

parallelogram, rectangle


WZ || XY and WX || ZY

WZZY, ZYXY, XYWX and WXWZ



A. A(–1, 3), B(1, 5), C(7, 5), D(5, 3)

parallelogram

A

CB

D


Try This

B. E(1, 5), F(7, 5), G(6, 1), H(2, 1)

trapezoid

E F

H G

EF || HG


Try This

C. W(4, 8), X(8, 2), Y(2, –2), Z(–2, 4)


X

W

Y

Z

ZW || YX and WX || ZY

WXZW, XYWX, YZXY and ZWYZ


Try This

D. R(–1, 1), S(3, 7), T(6, 5), U(2, –1)

parallelogram, rectangle R

S

U

T




Try This

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

Lesson Quiz