GUIDED PRACTICE for Examples 1 and 2

Use the distributive property to simplify or write an equivalent expression.

1. 2(w – 8) – 8(f + 2 + 3)2.

GUIDED PRACTICE for Examples 1 and 2

Use the distributive property to simplify or write an equivalent expression.

1. 2(w – 8)

= 2w – (2)(8)

= 2w – 16

– 8(f + 2 + 3)2.

= -8f + (-8)(2) + (-8)(3)

= -8f + -16 + -24

= -8f + -40

2.8 Coordinate Plane

2,4

5,1

-5

-5

5

5

2,2 1,7

Imagine the top surface of your desk stretching in every direction.

If it continued to spread , it would go right through your

neighbor . . .

. . . and then through the classroom walls . . .

Then you would have a plane.

In mathematics, a plane is a flat surface that goes on forever in

every direction.

We often use the coordinate plane.

The coordinate plane is divided by two number lines. One is

horizontal, like the number line you already know.

-5 50 10-10

The other is vertical, with up being the positive direction and

down being the negative direction.

-5 50 10-10

5

-5

The coordinate plane is filled with points . . .

. . . infinitely many points.

And somewhere among all those points is the point we call the

origin.

The origin is the point where the

two number lines meet.

-5 50 10-10

5

-5

The two number lines have special

names.

The horizontal number line is

called the x-axis.

x-5 50 10-10

5

-5

The vertical number line is

called the y-axis.

y

x-5 50 10-10

5

-5

To study a point, we need to know where to find it. So we give it

coordinates.

Coordinates are like an address. They tell you how you can get to a

point if you start at the origin.

yCoordinates are always written in parentheses, with the x-value first.

yx,

x-5 50 10-10

5

-5

yCoordinates written in

parentheses are called an

ordered pair.

yx,

x-5 50 10-10

5

-5

Consider the point which has coordinates,

(4, -2)

-5 50 10-10

5

-5

The first number tells you how far

to move to the side.

-5 50 10-10

5

-5

So the 4 in (4, -2) says we need to move 4 units to

the right.

Remember to start at the origin.

-5 50 10-10

5

-5

The second number tells you how far to move

up or down.

-5 50 10-10

5

-5

The –2 in (4, -2) tells you to move down two units.

2,4

-5 50 10-10

5

-5

To get to the origin from the origin, we don’t

move at all.

0,0

So the origin is designated by the ordered pair,

(0, 0)

-5 50 10-10

5

-5

The two number lines divide the plane into four

regions.

Quadrants are labeled with

Roman Numerals.

We call the regions

quadrants.

-5 50 10-10

5

-5

In Quadrant I, all numbers are

positive.

In Quadrant II, x-values are negative, while y-values are

positive.

In Quadrant III, x- and y-values are both negative.

In Quadrant IV, x-values are positive and y-values are

negative.

-5 50 10-10

5

-5

To plot a point

• Start at the origin (0,0)

• Go left or right along the x-axis

• Go up or down along the y-axis

Give the coordinates of each point:

Give the coordinates of each point:

3,2

2,3 4,2

1,5

Tell how you can find each point:

0,4

Remember to start at the origin!

7, 7

5,4

0, 3 6,5

From the origin, move to the right 8 units, then down 7 units.

6,4

Graph the points and tell which quadrant they are in :

0,4

7, 7

5,4

0, 3

6,5

6,4

EXAMPLE 3 Solve a Multi-Step Problem

Archaeology

On a field trip, students are exploring an archaeological site. They rope off a region to explore as shown. Identify the shape of the region and find its perimeter. The units on the scale are feet.

EXAMPLE 3 Solve a Multi-Step Problem

SOLUTION

STEP 1 Notice that points A, B, C, and D form a rectangle. Find the coordinates of the vertices.

STEP 2 Find the horizontal distance from A to B to find the length l.

x-coordinate of Bx-coordinate of A=l –

= –30 – 30 –60= = 60

A(–30, 20), B(30, 20), C(30, –20), D (–30, –20)

EXAMPLE 3 Solve a Multi-Step Problem

STEP 3 Find the vertical distance from A to D to find the width w.

STEP 4 Find the perimeter:

y-coordinate of Dy-coordinate of A=w –

= 20 – (–20) 40= = 40

2l + 2w = 2(60) + 2(40) = 200.

ANSWER

The region’s perimeter is 200 units 10 feet per unit = 2000 feet.

Assignment• Do. P. 96 #1-18, 24

• Use Graph Paper– 1st Grid: Do problem 1– 2nd Grid: Graph problems 11-18– 3rd Grid: Problem 24

• Remember to explain how to plot all of 11-18, plot the point and tell what quadrant it is in.