Name_________________
Date_______ Period_____
Pythagorean Theorem-Distance
1. Evan was biking on a trail. A map of the trail is shown. His brother timed his ride from
point A to point B.
A. What do the bold lines on the graph represent?
B. What type of triangle is formed by the lines?
C. How can you find the length of AC and BC ?
D. What are the lengths of the two lines?
E. Write an equation using the Pythagorean Theorem that you can use to find the length of AB .
Graph the ordered pair. Then find the distance c between the two points. Round to the nearest tenth.
2. (1, 3) and (-2, 4)
3. (0, -6) and (5, -1)
4. On the map, each unit represents 45 miles. West Point, New York, is
located at (1.5 ,2) and Annapolis, Maryland, is located at (-1.5, -1.5). What is
the approximate distance between West Point and Annapolis?
5. (1, 5) and (3, 1)
6. (4, 5) and (2,2)
7. Cromwell Field is located at (2.5, 3.5) and Dedeaux Field at (1.5, 4.5) on a map. If each
map unit is 0.1 miles, about how far apart are the fields?
8. An archaeologist at a dig sets up a coordinate system
using string. Two similar artifacts are found- one at (1,
4) and the other at (6, 2). How far apart were the two
artifacts? Round to the nearest tenth.
9. Jan set up a coordinate system with units of feet to
locate the position of the vegetables she planted in her
garden. She has a tomato plant at (1, 3) and a pepper
plant at (5, 6). How far apart are the two plants? Round
to the nearest tenth.
10. April is an avid chess player. She sets up a
coordinate system on her chess board so she can record
the position of the pieces during a game. In a recent
game, April noted that her king was at (4, 2) at the same
timer that her opponent’s king was at (3, 6). How far
apart were the two kings? Round to the nearest tenth.
11. A ferry sets sail from an island located at (-4, 6) on a
map. Its destination is Ferry Landing B at (6, 2). How far
will the ferry travel if each unit on the grid is 0.5 miles?
12. Travis uses a coordinate system with units of feet to
keep track of the locations of any object he finds with
his metal detector. One lucky day he found a ring at (3,
5) and an old coin at (1, 1). How far apart were the rings
and coin? Round to the nearest tenth.
13. Bryce is looking at a map of a theme park. The map
is laid out in a coordinate system Bryce is at (2, 3). The
roller coaster is at (-6, 5). How far apart is Bryce and the
roller coaster?
14. On a park map, the ranger station is located at (2.5,
3.5) and the nature center is located at (0.5, 4). Each
unit in the map is equal to 0.5 mile. What is the distance
between the ranger station and the nature center?
15. Cory makes a map of his favorite park, using a
coordinate system with units of yards. The old oak tree
is at (4, 2) and the granite boulder is at (-3, 5). How far
apart are the old oak tree and the granite boulder?
Round to the nearest tenth