The Algebra Teacher\'s Guide to Reteaching Essential Concepts and Skills

Name Date

WORKSHEET 4.16: USING THE DISTANCE FORMULA TO FIND

THE DISTANCE BETWEEN TWO POINTS

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To find the distance between two points, follow the steps below:

1. Use the distance formula:d=

√

(x 2 −x 1 )^2 +(y 2 −y 1 )^2

2. Replace each variable with the correctx-ory-coordinate.


3. Solve using the order of operations.

1

1

EXAMPLE

Find the distance between (1, 4) and (2, 3). In this problem, (1, 4) represents the first ordered

pair(x 1 ,y 1 )and (2, 3) represents the second ordered pair(x 2 ,y 2 ).

d=

√

(2−1)^2 +(3−4)^2

d=

√

(1)^2 +(−1)^2

d=

√

1 + 1

d=

√

2 ≈ 1. 414

Rounded to the nearest hundredth, the distance between (1, 4) and (2, 3) is about 1.41.

DIRECTIONS: Use the distance formula to find the distance between each pair of points.

Round to the nearest hundredth if necessary.

1. (2, 0), (7, 2) 2. (6, 1), (8, 5)


2. (3,−1), (0, 4) 4.(5, 4), (8, 2)

5.(−4,−5), (−2,−3) 6.(−2,−3), (6, 3)

7.(2,−7), (3,−3) 8.(−2, 3), (−1, 5)

CHALLENGE:Sammie said that the distance formula cannot be used to find

the distance between two points on a vertical line. Instead, she said that

you can subtract they-coordinates of two points on the vertical line. For

example, (0,3) and (0,10) are 7 units apart because 10− 3 =7. Do you

agree with her? Explain your answer.

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Copyright

©

2011 by Judith A. Muschla, Gary Robert Muschla, and Erin Muschla. All rights reserved.