Copyright © 2011 Pearson, Inc. P.2 Cartesian Coordinate System.
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Transcript of Copyright © 2011 Pearson, Inc. P.2 Cartesian Coordinate System.
Copyright © 2011 Pearson, Inc.
P.2Cartesian
Coordinate System
Copyright © 2011 Pearson, Inc. Slide P.2 - 2
What you’ll learn about
Cartesian Plane Absolute Value of a Real Number Distance Formulas Midpoint Formulas Equations of Circles Applications
… and whyThese topics provide the foundation for the material that
will be covered in this textbook.
Copyright © 2011 Pearson, Inc. Slide P.2 - 3
The Cartesian Coordinate Planeor Rectangular Coordinate System
Copyright © 2011 Pearson, Inc. Slide P.2 - 4
Quadrants
Copyright © 2011 Pearson, Inc. Slide P.2 - 5
Example Plotting Data on U.S. Exports to Mexico
The table gives the number of cars produced in the United States between 1997 and 2004. Plot the (year, annual production) ordered pairs in a rectangular coordinate system.
Copyright © 2011 Pearson, Inc. Slide P.2 - 6
Solution Plotting Data on U.S. Exports to Mexico
Copyright © 2011 Pearson, Inc. Slide P.2 - 7
Absolute Value of a Real Number
The absolute value of a real number a, is
|a |a, if a 0
a if a 0
0, if a 0
.
Copyright © 2011 Pearson, Inc. Slide P.2 - 8
Example Using the Definition of Absolute Value
Evaluate:
7
5
Copyright © 2011 Pearson, Inc. Slide P.2 - 9
Solution
Evaluate:
7 7
because 7 0, 7 7 7
5 5 5 because 3.14, 5 0
Copyright © 2011 Pearson, Inc. Slide P.2 - 10
Properties of Absolute Value
Let a and b be real numbers.
1. | a |0
2. | -a || a |
3. | ab || a || b |
4. a
b
| a |
| b |, b 0
Copyright © 2011 Pearson, Inc. Slide P.2 - 11
Distance Formula (Number Line)
Let a and b be real numbers.
The distance between a and b is a b .
Note that a b b a .
Copyright © 2011 Pearson, Inc. Slide P.2 - 12
Distance Formula (Coordinate Plane)
The distance d between points P x1 , y1 and Q x2 , y2 in the coordinate plane is
d x1 x2 2 y1 y2 2.
Copyright © 2011 Pearson, Inc. Slide P.2 - 13
The Distance Formula using the Pythagorean Theorem
Copyright © 2011 Pearson, Inc. Slide P.2 - 14
Example Finding the Distance Between Two Points
Copyright © 2011 Pearson, Inc. Slide P.2 - 15
Solution
d 2 5 2 7 3 2
3 2 4 2
9 16
25
5
Copyright © 2011 Pearson, Inc. Slide P.2 - 16
Midpoint Formula (Number Line)
The midpoint of the line segment
with endpoints a and b is
a b
2.
Copyright © 2011 Pearson, Inc. Slide P.2 - 17
Midpoint Formula (Coordinate Plane)
The midpoint of the line segment
with endpoints (a,b) and (c,d ) is
a c
2,b d
2
.
Copyright © 2011 Pearson, Inc. Slide P.2 - 18
Standard Form Equation of a Circle
The standard form equation of a circle
with center (h,k)and radius r is
(x h)2 (y k)2 r2 .
Copyright © 2011 Pearson, Inc. Slide P.2 - 19
Standard Form Equation of a Circle
Copyright © 2011 Pearson, Inc. Slide P.2 - 20
Example Finding Standard Form Equations of Circles
Find the standard form equation of the
circle with center (2, 3) and radius 4.
Copyright © 2011 Pearson, Inc. Slide P.2 - 21
Example Finding Standard Form Equations of Circles
(x h)2 (y k)2 r2 where h 2, k 3,and r 4.
Thus the equation is (x 2)2 (y 3)2 16.
Find the standard form equation of the
circlewith center (2, 3) and radius 4.
Copyright © 2011 Pearson, Inc. Slide P.2 - 22
Quick Review
2 2
2 2
2 2
-5 31. Find the distance between and .
4 2Use a calculator to evaluate the expression. Round answers
to two decimal places.
2. 8 6
-12 83.
2
4. 3 5
5. 2 5 1 3
Copyright © 2011 Pearson, Inc. Slide P.2 - 23
Quick Review Solutions
2 2
2 2
2 2
-5 31. Find the distance between and .
4 2Use a calculator to evaluate the expression. Round answers
to two decimal places.
2. 8 6
-12 83.
2
4. 3 5
5. 2
2.75
10
-2
5.83
3.5 1 3 61
