Page 165 - Math Course 2 (Book 1)

The Distance Formula

Mo. 5

Lesson 6 Key Concept

Distance Formula
KEY CONCEPTS:
1. Use the Distance Formula to determine
lengths on a coordinate plane. Words The distance d between two points with
coordinates (x , y ) and (x , y ), is given
1 1 2 2
2
by d = (x – y ) + (y – y ) 2
1
1
2
2
MO. 5 - L6a Model y
(x – y )
2
2
Using The Distance Formula (x – y ) d
1
1
Vocabulary A-Z 0 x
Let us learn some vocabulary

Distance Formula
Let’s Begin
The distance between two points on a coordinate
plane can be found using the distance formula.

Use the Distance Formula
2
c = a + b 2
b
Example

a
Find the distance between M(8, 4) and N(–6, –2).
A(x , y ) Round to the nearest tenth, if necessary.
1
1
2
d = (x – x ) + (y –y ) 2 Use the Distance Formula.
2 1 2 1
(y –y )
2 1
2
d = (x –x ) + (y – y ) 2 Distance Formula
2 1 2 1
(x – x ) B(x , y )
2 1 2 2 2 2 (x , y ) = (8, 4),
MN = (–6–8) + (–2 – 4) 1 1
(x , y ) = (–6, –2)
2
2
To f nd the length of a segment on a coordinate
2
plane, you can extend horizontal and vertical MN = (–14) + (–6) 2 Simplify.
segments from the vertices from a right triangle.
2
Then use the Pythagorean Theorem to f nd the MN = 196 + 36 Evaluate (–14) and
2
length of the segment. You can also use the (–6) .
Distance Formula, which is based on the
Pythagorean Theorem MN = 232 Add 196 and 36.
MN ≈ 15.2 Take the square root.

The distance between points M
Answer
and N is about 15.2 units.

157