Find the Distance Between Two Points
Find the distance between the points. Round your solution to the nearest
hundredth if necessary.
Student Help
VOCABULARY TIP
Vertices is the plural of
vertex. A triangle has
three vertices.
1. (2, 5), (0, 4)
2. (3, 2), (2, 2)
3. (8, 0), (0, 6)
4. (4, 2), (1, 3)
Check a Right Triangle
2
EXAMPLE
Determine whether the points
(3, 2), (2, 0), and (1, 4) are
vertices of a right triangle.
y
(1, 4)
5
d2
(3, 2)
1 d3
3
1
1
1
d1
x
(2, 0)
Solution
Use the distance formula to find the lengths of the three sides.
d1 (3
2
)2
(2
0
)2 12
22 1
4 5
d2 [3
(
1)]
2(2
4
)2 42(
2
)2 16
4 20
d3 [2
(
1)]
2(0
4
)2 32(
4
)2 9
6
1 25
Next find the sum of the squares of the lengths of the two shorter sides.
d12 d22 (5 )2 (20 )2
Substitute for d1 and d2.
5 20
Simplify.
25
Add.
The sum of the squares of the lengths of the two shorter sides is 25, which is
equal to the square of the length of the longest side, (25 )2.
ANSWER 䊳
By the converse of the Pythagorean theorem, the given points are
vertices of a right triangle.
Check a Right Triangle
Determine whether the points are the vertices of a right triangle.
5.
6.
y
(5, 5)
5
3
1
7.
y
(3, 5)
5
3
(1, 2)
1
(5, 2)
3
5 x
1
(0, 2)
3
1
3
(3, 6)
5
(5, 3)
1
y
5 x
12.7
(5, 3)
(1, 1)
1
3
The Distance Formula
5 x
731