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

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

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

Find Distance on the Coordinate Plane 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: The points are about 7.1 units apart. Example 1

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

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

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 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. Example 2

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

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. 0.76 mile B. 0.8 mile C. 1.13 miles D. 14.1 miles Example 2 CYP

Key Concept 4

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

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

Check Use the Pythagorean Theorem. The Distance Formula Check Use the Pythagorean Theorem. 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 ±7.1 ≈ c 7.1 = 7.1 The answer is correct. Example 3

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. 13.2 units Example 3 CYP

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

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

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. 10.2 units Example 4 CYP