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Splash Screen. Five-Minute Check (over Lesson 10–4) Then/Now New Vocabulary Key Concept: Distance Formula Example 1: Find the Distance Between Two Points Example 2: Real-World Example: Use the Distance Formula Concept Summary: Formulas Example 3: Find the Perimeter. Lesson Menu.

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  1. Splash Screen

  2. Five-Minute Check (over Lesson 10–4) Then/Now New Vocabulary Key Concept: Distance Formula Example 1: Find the Distance Between TwoPoints Example 2: Real-World Example: Use the Distance Formula Concept Summary: Formulas Example 3: Find the Perimeter Lesson Menu

  3. What is the length of the hypotenuse of a right triangle with sides a = 8 and b = 15? A.c = 16 B.c = 17 C.c = 18 D.c = 20 5-Minute Check 1

  4. What is the length of the hypotenuse of a right triangle with sides a = 6 and b = 12? A.c = 13.1 B.c = 13.2 C.c = 13.3 D.c = 13.4 5-Minute Check 2

  5. The lengths of three sides of a triangle are given. Determine whether the triangle is a right triangle. a = 7 b = 24 c = 25 A. yes B. no 5-Minute Check 3

  6. The lengths of three sides of a triangle are given. Determine whether the triangle is a right triangle. a = 10b = 12c = 15 A. yes B. no 5-Minute Check 4

  7. A computer screen has a diagonal of 14 inches. The width of the screen is 11 inches. Find the height of the screen. A. 8.8 in. B. 8.7 in. C. 8.6 in. D. 8.5 in. 5-Minute Check 5

  8. You found the slope of a line passing through two points on a coordinate plane. (Lesson 8–6) • Use the Distance Formula to find the distance between two points on a coordinate plane. • Apply the Distance Formula to solve problems about figures on the coordinate plane. Then/Now

  9. Distance Formula Vocabulary

  10. Concept A

  11. Find the Distance Between Two Points Find the distance between M(8, 4) and N(–6, –2). Round to the nearest tenth, if necessary. Use the Distance Formula. Distance Formula (x1, y1) = (8, 4), (x2, y2) = (–6, –2) Simplify. Evaluate (–14)2 and (–6)2. Example 1

  12. Find the Distance Between Two Points Add 196 and 36. Take the square root. Answer: The distance between points M and N is about 15.2 units. Example 1

  13. Find the distance between A(–4, 5) and B(3, –9). Round to the nearest tenth, if necessary. A. 4.1 units B. 8.1 units C. 14.0 units D. 15.7 units Example 1

  14. Use the Distance Formula SOCCER Javy kicks a ball from a position that is 2 yards behind the goal line and 4 yards from the sideline (–2, 4). The ball lands 8 yards past the goal line and 2 yards from the same sideline (8, 2). What distance, to the nearest tenth, was the ball kicked? Example 2

  15. Distance Formula (x1, y1) = (–2, 4) (x2, y2) = (8, 2) Use the Distance Formula Understand You know the coordinates of the two locations and that each unit represents 1 yard. You need to find the distance between the two points. Plan Use the Distance Formula to find the distance the ball was kicked. Solve Example 2

  16. Simplify. Evaluate powers. Simplify. Use the Distance Formula d ≈ 10.2 Answer: Javy kicked the ball 10.2 yards CheckThe distance is slightly greater than 10 yards, so the answer is reasonable.  Example 2

  17. MAPSThe map of a college campus shows Gilmer Hall at (7, 3) and Watson House dormitory at (5, 4). If each unit on the map represents 0.1 mile, what is the distance between these buildings? A. 0.2 mi B. 0.5 mi C. 2.2 mi D. 5 mi Example 2

  18. Concept B

  19. Find the Perimeter GEOMETRY Classify ΔXYZ by its sides. Then find its perimeter to the nearest tenth. Step 1 Use the Distance Formula to find the length of each side of the triangle. Example 3

  20. Side XY: X(–5, 1), Y(–2, 4) Find the Perimeter Distance Formula (x1, y1) = (–5, 1), (x2, y2) = (–2, 4) Simplify. Evaluate powers. Simplify. Example 3

  21. Side YZ: Y(–2, 4), Z(–3, –3) Find the Perimeter Distance Formula (x1, y1) = (–2, 4), (x2, y2) = (–3, –3) Simplify. Evaluate powers. Simplify. Example 3

  22. Side ZX: Z(–3, –3), X(–5, 1) Find the Perimeter Distance Formula (x1, y1) = (–3, –3), (x2, y2) = (–5, 1) Simplify. Evaluate powers. Simplify. Example 3

  23. Find the Perimeter None of the sides are congruent. So, ΔXYZ is scalene. Step 2 Add the lengths of the sides to find the perimeter. Answer: The triangle is scalene. The perimeter is about 15.8 units. Example 3

  24. GEOMETRY Find the perimeter of ΔXYZ to the nearest tenth. A. 21.3 units B. 14.6 units C. 13.4 units D. 10.9 units Example 3

  25. End of the Lesson

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