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Main Idea and New Vocabulary
Example 1: Find Distance on the Coordinate Plane
Example 2: Real-World Example
Key Concept: Distance Formula
Example 3: The Distance Formula
Example 4: The Distance Formula
• Find the distance between two points on the coordinate plane.
• Distance Formula
Find Distance on the Coordinate Plane
Graph the ordered pairs (0, –6) and (5, –1). Then find the distance between the points.
Find Distance on the Coordinate Plane
Answer: The points are about 7.1 units apart.
a2 + b2 = c2 Pythagorean Theorem
52 + 52 = c2 Replace a with 5 and b with 5.
50 = c2 52 + 52 = 25 + 25 or 50
Definition of square root
±7.1 ≈ c Use a calculator.
A. 7.1
B. 7.8
C. 8.1
D. 8.6
Graph the ordered pairs (4, 5) and (–3, 0). Then find the distance between the points.
CITY MAPS Reed lives in Seattle, Washington. One unit on this map is 0.08 mile. Find the approximate distance he drives between Broad Street at Denny Way (–1, 0) and Broad Street at Dexter Avenue North (4, 5).
Let c represent the distance between Denny Way and Dexter Ave along Broad Street. Then a = 5 and b = 5.
a2 + b2 = c2 Pythagorean Theorem
52 + 52 = c2 Replace a with 5 and b with 5.
50 = c2 52 + 52 = 25 + 25 or 50
Definition of square root
±7.1 ≈ c Use a calculator.
Answer: Since each map unit equals 0.08 mile, the distance that he drives is 7.1 • 0.08 or about 0.57 mile.
A. 0.76 mile
B. 0.8 mile
C. 1.13 miles
D. 14.1 miles
CITY MAPS One unit on the map is 0.08 mile. Find the approximate distance along Broad Street between the points at (–4, –3) and (6, 7).
The Distance Formula
Use the Distance Formula to find the distance between points C(4, 8) and D(–1, 3). Round to the nearest tenth if necessary.
Answer: So, the distance between points C and D
is about 7.1 units.
The Distance Formula
Distance Formula
(x1, y1) = (4, 8), (x2, y2) = (–1, 3)
Simplify.
Evaluate (–5)2.
Add 25 and 25.
Use a calculator.
The Distance Formula
a2 + b2 = c2 Pythagorean Theorem
52 + 52 = c2 Replace a with 5 and b with 5.
50 = c2 52 + 52 = 25 + 25 or 50
c Definition of square root
CheckUse the Pythagorean Theorem.
±7.1 ≈ c 7.1 = 7.1 The answer is correct.
A. 2.2 units
B. 3.9 units
C. 8.1 units
D. 13.2 units
Use the Distance Formula to find the distance between the points R(0, –6) and S(–2, 7). Round to the nearest tenth if necessary.
Use the Distance Formula to find the distance between the points G(–3, –2) and H(–6, 5). Round to the nearest tenth if necessary.
The Distance Formula
The Distance Formula
Answer: So, the distance between points G and H is about 7.6 units.
Distance Formula
(x1, y1) = (–3, –2),
(x2, y2) = (–6, 5)
Simplify.
Evaluate (–3)2 and (7)2.
Add 9 and 49.
Use a calculator.
A. 6 units
B. 6.3 units
C. 10 units
D. 10.2 units
Use the Distance Formula to find the distance between the points J(–8, –1) and K(2, 1). Round to the nearest tenth if necessary.
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