2. 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
Lesson Menu

3. Find the distance between two points on the coordinate plane.
Distance Formula
Main Idea/Vocabulary

4. Find Distance on the Coordinate Plane
Graph the ordered pairs (0, –6) and (5, –1). Then find the distance between the points.
Example 1

5. Find Distance on the Coordinate Plane
a2 + b2 = c2 Pythagorean Theorem
= c2 Replace a with 5 and b with 5.
50 = c = or 50
Definition of square root
±7.1 ≈ c Use a calculator.
Answer: The points are about 7.1 units apart.
Example 1

6. Graph the ordered pairs (4, 5) and (–3, 0)
Graph the ordered pairs (4, 5) and (–3, 0). Then find the distance between the points.
A. 7.1
B. 7.8
C. 8.1
D. 8.6
Example 1 CYP

7. CITY MAPS Reed lives in Seattle, Washington. One unit on this map is 0
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).
Example 2

8. a2 + b2 = c2 Pythagorean Theorem
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
= c2 Replace a with 5 and b with 5.
50 = c = or 50
Definition of square root
±7.1 ≈ c Use a calculator.
Example 2

9. Answer:. Since each map unit equals 0
Answer: Since each map unit equals 0.08 mile, the distance that he drives is 7.1 • 0.08 or about 0.57 mile.
Example 2

10. CITY MAPS One unit on the map is 0. 08 mile
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).
A mile
B. 0.8 mile
C miles
D miles
Example 2 CYP

11. Key Concept 4

12. 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.
Example 3

13. 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.
Answer: So, the distance between points C and D is about 7.1 units.
Example 3

14. Check Use the Pythagorean Theorem.
The Distance Formula
Check Use the Pythagorean Theorem.
a2 + b2 = c2 Pythagorean Theorem
= c2 Replace a with 5 and b with 5.
50 = c = or 50
c Definition of square root
±7.1 ≈ c 7.1 = 7.1 The answer is correct.
Example 3

15. 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.
A. 2.2 units
B. 3.9 units
C. 8.1 units
D units
Example 3 CYP

16. The Distance Formula
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.
Example 4

17. Answer: So, the distance between points G and H is about 7.6 units.
The Distance Formula
Distance Formula
(x1, y1) = (–3, –2), (x2, y2) = (–6, 5)
Simplify.
Evaluate (–3)2 and (7)2.
Add 9 and 49.
Use a calculator.
Answer: So, the distance between points G and H is about 7.6 units.
Example 4

18. 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.
A. 6 units
B. 6.3 units
C. 10 units
D units
Example 4 CYP