Page 174 - Math Course 2 (Book 1)

Radical Expressions: The Distance Formula

Mo. 5

Lesson 8
Let’s Begin

KEY CONCEPTS:
1. Find the distance between two points on Distance Between Two Points
the coordinate plane.
2. Find a point that is a given distance from a
second point on a plane. Example

Find the distance between the points at (1, 2) and
MO. 5 - L8a (–3, 0).

Find the Distance Between d = (x –x ) + (y – y ) 2
2
2 1 2 1 Distance Formula
Two Points (x , y ) = (1, 2), and
1
1
2
Distance Formula = (–3–1) + (0 – 2) 2 (x , y ) = (–3, 0)
2
2
2
You can f nd the distance between any two points = (–4) + (–2) 2 Simplify.
in the coordinate plane using the Distance Formula
which is based on the Pythagorean Theorem. = 20 Evaluate squares
and simplify.

2
c = a + b 2 Answer = 2 5 or about 4.47 units.
b

a
Real World Example
A(x , y )
1 1
BIATHLON
2
d = (x – x ) + (y –y ) 2 Julianne is sighting her rif e for an
2 1 2 1
(y –y ) upcoming biathlon competition.
2 1 Her f rst shot is 2 inches to the
right and 7 inches below the bull’s-
(x – x ) B(x , y ) eye. What is the distance between
2 1 2 2
the bull’s-eye and where her f rst shot hit the target?
Key Concept y

Distance Formula

Words The distance d between two points with

coordinates (x , y ) and (x , y ), is given (0, 0)
1 1 2 2
2
by d = (x – y ) + (y – y ) 2 0
2 1 2 1 x
Model y
A B
(x – y ) (x – y )
1 1 2 2
0 x (2, –7)

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