Name
Class
Date
Lesson 1-7 Distance in the Coodinate Plane
Lesson Objective
Common Core Standards
To graph points and to use the
Pythagorean Theorem to find distances
in the coordinate plane
Geometry: 8.G.7, 8.G.8
Vocabulary
The x-axis is a horizontal number line.
The y-axis is a vertical number line.
Quadrants are the four regions of a coordinate plane formed by the x- and y-axes.
The origin is where the axes intersect on a coordinate plane.
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A coordinate plane is a grid formed by the intersection of two number lines.
An ordered pair gives the coordinates of the location of a point.
The x-coordinate tells the number of horizontal units a point is from the origin.
The y-coordinate tells the number of vertical units a point is from the origin.
1 Finding Distance on a Coordinate Plane Find the distance between points
A(22, 4) and B(4, 24).
horizontal leg: 4 2 22 5 6 units
A(2, 4)
vertical leg: 4 2 24 5 8 units
a2 1 b2 5 c2 ← Pythagorean Theorem
6 2 1 8 2 5 c2
← Substitute.
36 1 64 5 c2
100 5 c2
100 5
4
(4, 4)
y
2
2
4 2
← Simplify.
2
← Add.
4
4 x
B(4, 4)
c ← Find the positive square root of each side.
2
10 5 c
The distance between A(22, 4) and B(4, 24) is
14
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Course 3 Lesson 1-7
10 units.
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
Example
Daily Notetaking Guide
10/10/12 4:19 PM
Name
Class
Date
2 Multiple Choice The park is 4 kilometers west of the bus station. The
grocery store is 7 kilometers south of the bus station. To the nearest
kilometer, how far is the grocery store from the park?
A. 5 km
B. 6 km
C. 7 km
D. 8 km
← Use the Pythagorean Theorem.
a2 1 b2 5 c2 4 2 1 7 2 5 c 2
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16 1 49 5 c2
65
5 c2
65
5
65
y Bus
Station
x
Park
← Substitute
← Simplify.
Grocery
Store
← Add.
← Find the positive square root of each side.
c2 8.062257748 ← Use a calculator.
← Simplify.
c¯ 8 The correct answer is choice
D
.
Quick Check
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
1. Find the distance between points (2, 1) and (7, 9). If necessary, round to
the nearest tenth.
a2 1 b2 5 c2
52 1 8 2 5 c 2
25 1 64 5 c2
89 5 c2
89 5 c 2
c ¯ 9.4
2. Your school is 3 miles south of your house. The park is 5 miles east
of your school. To the nearest mile, how far is your house from the park?
6 miles
Daily Notetaking Guide
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