Name: Date: Lesson 7.2 Understanding the Distance Formula
Solve. Show your work. Round your answers to the nearest tenth if
necessary.
y
1. Points P (24, 3) and Q (4, 23) are plotted
on a coordinate plane. Find the exact
distance between points P and Q.
P (4, 3)
3
2
1
4 3 2 1 0
1
1
2
3
4
5
x
2
3
Q (4, 3)
2. Find the distance between each pair of points. Which pair of points are the
least distance apart?
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a) A(3, 22), B(0, 24) b) C(4, 2), D(2, 26)
c) E(3, 23), F(27, 8) d) G(21, 24), H(22, 25)
3. Samantha plots the points P (23, 4), Q (3, 3),
and R (4, 23) on a coordinate plane. She
joins the three points to form triangle PQR.
Is the triangle a right triangle? Explain.
y
P (3, 4)
4
Q (3, 3)
3
2
1
3 2 1 0
1
1
2
3
4
x
2
3
R (4, 3)
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Name: Date: Use the data in the diagram for questions 4 to 6. Each unit on the grid
equals 1 kilometer.
y
Bank
(5, 4)
4
3
2
1
5 4 3 2 1 0
1
Post Office
(4, 3)
Home
(1, 2)
1
2
3
4
5
x
2
3
4
Cinema
(1, 4)
School
(3, 4)
4. Find the approximate distance from Mary’s home to each of the following
locations.
a) Bank b) Cinema c) Post Office d) School
5. Which three locations are the same distance from Mary’s home?
6. On a particular day, Mary traveled from her home to school. After school,
she went to the post office to mail a letter. Then, she went home. Find the
total distance she traveled.
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10 Chapter 7 Lesson 7.2
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Name: Date: Solve. Show your work.
7. Town A and Town B are located at the points shown in the diagram.
Mr. Appleton wants to drive from Town A to Town B. He can choose
between the route that takes him through Towns P and Q, or the route that
takes him through Town R. Each unit on the grid equals 1 kilometer.
y
5
Town R
(3, 4)
Town A
(2, 3)
4
3
2
Town P
(3, 1)
1
4 3 2 1 0
1
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Town B
(4, 2)
2
1
2
3
4
x
Town Q
(0, 2)
a) Which is the shorter route?
b) What is the difference in distances of the two routes?
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Name: Date: Solve. Show your work. Round your answer to the nearest tenth.
8. The positions of a boat and a lighthouse are shown on the grids. Each unit
on the grid equals 1 mile.
2
y
4
3
Boat
(2, 3)
2
1
4 3 2 1 0
1
1
2
3
4
x
2
3
4
5
a) How far is the boat from the lighthouse?
b)The boat takes 20 minutes to travel to the lighthouse. Find the speed
of the boat in miles per hour.
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Lighthouse
(3, 4)
12 Chapter 7 Lesson 7.2
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