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

Course 3

7-5 Coordinate Geometry

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

Course 3

7-5 Coordinate Geometry

Learn to identify polygons in the coordinate plane.

Course 3

7-5 Coordinate Geometry

TB P. 347-351

Vocabularyslope

rise

run

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Course 3

7-5 Coordinate Geometry

Course 3

7-5 Coordinate Geometry

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.

Course 3

7-5 Coordinate Geometry

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

slope =vertical change

horizontal changerise run=

Course 3

7-5 Coordinate Geometry

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!

Course 3

7-5 Coordinate Geometry

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

Course 3

7-5 Coordinate Geometry

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

ZA

negative slope;

slope of ZA = = ––1 2

12

Additional Example 1B: Finding the Slope of a Line

Course 3

7-5 Coordinate Geometry

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

BC

slope of BC is undefined

Additional Example 1C: Finding the Slope of a Line

Course 3

7-5 Coordinate Geometry

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

DM

slope of DM = 0

Additional Example 1D: Finding the Slope of a Line

Course 3

7-5 Coordinate Geometry

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

Course 3

7-5 Coordinate Geometry

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

Course 3

7-5 Coordinate Geometry

Additional Example 2 Continued

The slopes are equal. =35

35

The slopes have a product

of –1: • – = –132

2 3

GH || PQ

EF CD

Which lines are parallel? Which lines are perpendicular?

Course 3

7-5 Coordinate Geometry

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

Course 3

7-5 Coordinate Geometry

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

Course 3

7-5 Coordinate Geometry

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).

Course 3

7-5 Coordinate Geometry

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

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8

7

Course 3

7-5 Coordinate Geometry

– 10 3

MN, RQ