Name: _____________________ Date: ____________Period: _______ Hom ew ork P age 48
Distance Formula Assignment and Notes
Coordinate Points: (𝑥𝑥1 , 𝑦𝑦1 ) 𝑎𝑎𝑎𝑎𝑎𝑎 (𝑥𝑥2 , 𝑦𝑦2 )
Example #1:
𝐴𝐴(3 , −1) 𝑎𝑎𝑎𝑎𝑎𝑎 𝐵𝐵(2 , −2)
Distance Formula: 𝒅𝒅 = �(𝑥𝑥2 − 𝑥𝑥1 )2 + (𝑦𝑦2 − 𝑦𝑦1 )2
Example #2:
𝐶𝐶(−2 , 1) 𝑎𝑎𝑎𝑎𝑎𝑎 𝐷𝐷(6 , −3)
Use the distance formula to find the distance between each pair of points. If necessary,
round your answer to the nearest tenth.
1.) (0 , 3) 𝑎𝑎𝑎𝑎𝑎𝑎 (−2 , 0)
2.) (−3 , 2) 𝑎𝑎𝑎𝑎𝑎𝑎 (−4 , 7)
3.) (−4 , 2) 𝑎𝑎𝑎𝑎𝑎𝑎 (−2 , −3)
4.) (−2 , −3) 𝑎𝑎𝑎𝑎𝑎𝑎 (−1 , −4)
5.) (2 , 7) 𝑎𝑎𝑎𝑎𝑎𝑎 (−3 , −5)
6.) (2 , 7) 𝑎𝑎𝑎𝑎𝑎𝑎 (3 , 5)
For #7 – 11; Find the distance between the two cities using the information in the table, which is from a
coordinate system used for calculating long-distance telephone rates.
Buffalo, NY
(5075,2326)
Omaha, NE
(6687, 4595)
Chicago, IL
(5986, 3426)
Providence, RI
(4550, 1219)
Dallas, TX
(8436, 4034)
San Diego, CA
(9468, 7629)
Miami, FL
(8351, 527)
Seattle, WA
(6336, 8896)
7) Buffalo and Dallas
8) Chicago and Seattle
10) Providence and San Diego
9) Miami and Omaha
11) Buffalo and Providence
For #12-14: Use the grid at the right.
12.) Graph the coordinates
𝑋𝑋(−2 , 4) ; 𝑌𝑌(6 , −3) ; 𝑍𝑍(2 , −2)
13.) Find the lengths of the sides ����
𝑋𝑋𝑋𝑋 , ����
𝑌𝑌𝑌𝑌 , ����
𝑋𝑋𝑋𝑋 to the
nearest tenth.
����=_________ 𝑌𝑌𝑌𝑌
���� =_________ 𝑋𝑋𝑋𝑋
����=__________
𝑋𝑋𝑋𝑋
14.) Show that the sum of the lengths of the two
shortest sides is greater than the length of the third
side.