Math Connects, Course 3 77

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.Geometry: Distance on the Coordinate Plane

A coordinate plane is formed by two number lines that

form right angles and intersect at their points.

The point of intersection of the two number lines is the origin.

The number line is the y-axis.

The number line is the x-axis.

The number lines separate the coordinate plane into

sections called quadrants.

Any point on the coordinate plane can be graphed by using an ordered pair of numbers.

The number in the ordered pair is called the

x-coordinate.

The number of an ordered pair is the

y-coordinate.

Another name for the is abscissa.

Another name for the is ordinate.

BUILD YOUR VOCABULARY (pages 62–63)

EXAMPLE Name an Ordered Pair

Name the ordered pair for point A.

• Start at the origin.

• Move right to fi nd the

of point A, which is .

(continued on the next page)

3–7

y

x

A

MAIN IDEAS

• Graph rational numbers on the coordinate plane.

• Find the distance between points on the coordinate plane.

ORGANIZE ITOn Lesson 3-7 of your Foldable, explain in writing how to use ordered pairs to fi nd the distance between two points.

Chapter 3Real Numbers and the Pythagorean Theorem

®

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3–7

78 Math Connects, Course 3

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• Move up to fi nd the ,which is .

So, the ordered pair for point A is .

Check Your Progress Name the ordered y

x

A

pair for point A.

EXAMPLES Graphing Ordered Pairs

Graph and label each point on the same coordinate plane.

J (-3, 2.75)

• Start at and move

units to the .

Then move units.

• Draw a dot and label it

.

K (4, -1 1 _ 4 )

• Start at and move units to the .

Then move units.

• Draw a dot and label it .

Check Your Progress y

xO

Graph and label each point on the same coordinate plane.

a. J (-2.5, 3.5)

b. K (2, -2 1 _ 2 )

y

x

K 4, 1

J( 3, 2.75)

14)(

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3–7

Math Connects, Course 3 79

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.EXAMPLE Find the Distance on the Coordinate Plane

Graph the ordered pairs (0, -6) and (5, -1) . Then fi nd the distance between the points.

Let c = distance between the two points, a = 5, and b = 5.

c 2 = a 2 + b 2 Pythagorean Theorem

c 2 = + Replace a with and b with .

c 2 = + =

√ � c 2 = Defi nition of

c = Simplify.

The points are about apart.

Check Your Progress Graph the ordered pairs (0, -3) and ( 2, -6) . Then fi nd the distance between the points.

REMEMBER IT You can use the Pythagorean Theorem to fi nd the distance between two points on a coordinate plane.

x

y

O

(5, 1)

(0, 6)

y

xO

HOMEWORKASSIGNMENTPage(s):

Exercises:

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