2.8 coord. plane 1
TRANSCRIPT
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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.
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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
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2.8 Coordinate Plane
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2,4
5,1
-5
-5
5
5
2,2 1,7
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Imagine the top surface of your desk stretching in every direction.
If it continued to spread , it would go right through your
neighbor . . .
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. . . and then through the classroom walls . . .
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Then you would have a plane.
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In mathematics, a plane is a flat surface that goes on forever in
every direction.
We often use the coordinate plane.
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The coordinate plane is divided by two number lines. One is
horizontal, like the number line you already know.
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-5 50 10-10
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The other is vertical, with up being the positive direction and
down being the negative direction.
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-5 50 10-10
5
-5
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The coordinate plane is filled with points . . .
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. . . infinitely many points.
And somewhere among all those points is the point we call the
origin.
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The origin is the point where the
two number lines meet.
-5 50 10-10
5
-5
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The two number lines have special
names.
The horizontal number line is
called the x-axis.
x-5 50 10-10
5
-5
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The vertical number line is
called the y-axis.
y
x-5 50 10-10
5
-5
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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.
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yCoordinates are always written in parentheses, with the x-value first.
yx,
x-5 50 10-10
5
-5
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yCoordinates written in
parentheses are called an
ordered pair.
yx,
x-5 50 10-10
5
-5
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Consider the point which has coordinates,
(4, -2)
-5 50 10-10
5
-5
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The first number tells you how far
to move to the side.
-5 50 10-10
5
-5
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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
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The second number tells you how far to move
up or down.
-5 50 10-10
5
-5
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The –2 in (4, -2) tells you to move down two units.
2,4
-5 50 10-10
5
-5
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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
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The two number lines divide the plane into four
regions.
Quadrants are labeled with
Roman Numerals.
We call the regions
quadrants.
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5
-5
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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
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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
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Give the coordinates of each point:
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Give the coordinates of each point:
3,2
2,3 4,2
1,5
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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
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Graph the points and tell which quadrant they are in :
0,4
7, 7
5,4
0, 3
6,5
6,4
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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.
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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)
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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.
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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.