Pre-Algebra Chapter 9

Example 1
Use the Distance Formula
Find the distance between G(3, 1)
and H(2, 4). Round to the nearest
tenth, if necessary.
G(3, 1)
y
O
x
Study Tip
Substitution
You can use either point
as (x 1
, y 1
). The distance
will be the same.
Use the Distance Formula.
d (x 2
x 1
y ) 2 ( 2
y 1
) 2
Distance Formula
GH [2 3)] ( 2 (4 1) 2 (x 1
, y 1
) (3, 1), (x 2
, y 2
) (2, 4)
GH (5) 2 (5) 2
Simplify.
GH 25 5 2
Evaluate 5 2 and (5) 2 .
GH 50 Add 25 and 25.
GH 7.1
Take the square root.
The distance between points G and H is about 7.1 units.
H(2, 4)
The Distance Formula can be used to solve geometry problems.
Example 2
Use the Distance Formula to Solve a Problem
GEOMETRY Find the perimeter of ABC
to the nearest tenth.
First, use the Distance Formula to find
the length of each side of the triangle.
Side AB : A(2, 3), B(2, 2)
d (x x 2
1
) 2 (y 2
y 1
) 2
AB [2 2)] ( 2 ) (2 3
2
AB (4) 2 (1) 2
AB 16 1
AB 17
A(2, 3)
O
y
B(2, 2)
C(0, 3)
x
Study Tip
Common
Misconception
To find the sum of square
roots, do not add the
numbers inside the square
root symbols.
17 29
40 86
Side BC : B(2, 2), C(0, 3) Side CA : C(0, 3), A(2, 3)
d (x x 2
1
) 2 (y 2
y 1
) 2
d (x x 2
1
) 2 (y 2
y 1
) 2
BC [0 ] 23 ( 2)
CA [2
0] 2 3)) (3 (
2
BC (2) 2 ) (5 CA (2) 2 (6) 2
BC 4 25
CA 4
36
BC 29
CA 40
Then add the lengths of the sides to find the perimeter.
17 29 40 4.123 5.385 6.325
15.833
The perimeter is about 15.8 units.
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Lesson 9-6 The Distance and Midpoint Formulas 467