7-5 Coordinate Geometry Course 3 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

7-5 Coordinate Geometry

Course 3

Warm Up

Problem of the Day

Lesson Presentation

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

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parallel

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

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Learn to identify polygons in the coordinate plane.

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Vocabularyslope

rise

run

Insert Lesson Title Here

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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.

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

slope =vertical change

horizontal changerise run=

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

When a nonzero number is divided by zero, the quotient is undefined. There is no answer.

Remember!

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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.

XY

positive slope;

slope of XY = = –5–4

54

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ZA

negative slope;

slope of ZA = = ––1 2

12

Additional Example 1B: Finding the Slope of a Line

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BC

slope of BC is undefined

Additional Example 1C: Finding the Slope of a Line

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DM

slope of DM = 0

Additional Example 1D: Finding the Slope of a Line

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Check It Out: Example 1A


AB A

C

B

D

FE

HG

positive slope;

slope of AB = 1 8

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CD

slope of CD is undefined

Check It Out: Example 1B


A

C

B

D

FE

HG

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EF

slope of EF = 0

Check It Out: Example 1C


A

C

B

D

FE

HG

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GH

Check It Out: Example 1D


A

C

B

D

FE

HG

negative slope;

slope of GH = = ––1 3

13

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Slopes of Parallel and Perpendicular Lines

Two lines with equal slopes are parallel.

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

If a line has slope , then a line

perpendicular to it has slope – .

Helpful Hint a b b

a

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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

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Additional Example 2 Continued

The slopes are equal. =35

35

The slopes have a product

of –1: • – = –132

2 3

GH || PQ

EF CD


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Check It Out: 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

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CD || EF

GH AB

A

C

B

D

F

E

K

JH

G

Check It Out: Example 2 Continued


The slopes are equal. =–2 3

–2 3

The slopes have a product

of –1: • – = –123

3 2

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Additional Example 3A: Using Coordinates to Classify Quadrilaterals

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

parallelogram

CD || BA and BC || AD

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

parallelogram, rectangle, rhombus, square

Additional Example 3B: Using Coordinates to Classify Quadrilaterals

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

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Check It Out: Example 3A


A(–1, 3), B(1, 5), C(7, 5), D(5, 3)

parallelogram

A

CB

D

CD || BA and BC || AD

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

trapezoid

E F

H G

EF || HG

Check It Out: Example 3B


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Rectangle WXYZ with W(–2, 2), X(3, 2), and Y(3, –4)

Step 2 Complete the figure to find the missing vertex.

Additional Example 4: Finding the Coordinates of a Missing Vertex

Find the coordinates of the missing vertex.

W

Y

X

Z

Step 1 Graph and connect the given points.

The coordinates of Z are (–2, –4).

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Rectangle JKLM with J(– 1, 2), K(4, 2), and L(4, –1)

Step 2 Complete the figure to find the missing vertex.

Additional Example 4B: Finding the Coordinates of a Missing Vertex

Find the coordinates of the missing vertex.

J

L

K

M

Step 1 Graph and connect the given points.

The coordinates of M are (–1, –1).

Lesson Quiz

Determine the slope of each line.

1. PQ

2. MN

3. MQ

4. NP

5. Which pair of lines are parallel?

1

Insert Lesson Title Here

8

7

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– 10 3

MN, RQ

Documents

7-5 Coordinate Geometry Course 3 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation