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Lesson 9.5-The Distance Formula

Lesson 9.5-The Distance Formula. HW:9.5/ 1-14. Isosceles Right ∆Theorem. 45 ° – 45 ° – 90 ° Triangle In a 45 ° – 45 ° – 90 ° triangle the hypotenuse is the square root of two * as long as each leg. Theorem. 30 ° – 60 ° – 90 ° Triangle

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Lesson 9.5-The Distance Formula

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  1. Lesson 9.5-The Distance Formula HW:9.5/ 1-14

  2. Isosceles Right ∆Theorem • 45° – 45° – 90° Triangle • In a 45° – 45° – 90° triangle the hypotenuse is the square root of two * as long as each leg

  3. Theorem • 30° – 60° – 90° Triangle • In a 30° – 60° – 90° triangle, the hypotenuse is twice as long as the shorter leg, and the longer leg is the square root of three times as long as the shorter leg

  4. Problem Solving Strategy Know the basic triangle rules Solve for the other sides Set known information equal to the corresponding part of the basic triangle

  5. New Material THE DISTANCE FORMULA

  6. Coordinate Geometry

  7. Coordinate Geometry - Investigation Use the Pythagorean Theorem to find the length of the segment c 2 4 6 2

  8. Coordinate Geometry The Distance Formula is based on the Pythagorean Theorem (AB)2 = (x2 - x1)2 + (y2 - y1)2 The distance between points A(x1,y1) and B(x2,y2) is given by

  9. Coordinate Geometry - Example

  10. Exploration • Get your supplies - Graph Paper - ruler - pencil • Create a large XY coordinate grid

  11. Exploration Copy and label these points onto your graph paper, include the coordinates of each point

  12. Exploration • Find the distance between the listed attractions • Use the Pythagorean theorem. • Draw right triangle if necessary.

  13. Bumper cars to sledge hammer • (-4, -3) to (2, -3) y x Distance = 6

  14. b. Ferris Wheel and Hall of Mirrors (0, 0) and (3, 1) Use the Pythagorean Theorem y = =10 c 1 x 3

  15. Using the points and Pythagorean theorem = DISTANCE FORMULA b. Ferris Wheel and Hall of Mirrors (0, 0) and (3, 1)

  16. c. Refreshment Stand to Ball Toss(-5, 2) to (-2, -2) Use the Pythagorean theorem y = =25 c x 4 3

  17. Using the points and Pythagorean theorem = DISTANCE FORMULA c. Refreshment Stand to Ball Toss (-5, 2) to (-2, -2)

  18. d. Bumper Cars to Mime Tent(-4, -3) to (3, 3) Use the Pythagorean theorem y = =85 c 6 x 7

  19. d. Bumper Cars to Mime Tente. (-4, -3) to (3, 3)

  20. Exploration If your car is parked at the coordinates (17, -9), and each grid unit represents 0.1 mile, how far is from your car to the refreshment stand? Try to complete this without plotting the location of your car. Car to Refreshment stand (17, -9) to (-5, 2) units *0.1 miles ≈2.46 Miles

  21. Find the distance between the points at (1, 2) and (–3, 0).

  22. Find the distance between the points at (2, 3)and (–4, 6).

  23. Find the distance between the points at (5, 4) and (0, –2).

  24. Horseshoes Marcy is pitching a horseshoe in her local park. Her first pitch is 9 inches to the left and 3 inches below the pin. What is the distance between the horseshoe and the pin? &

  25. Homework Lesson 9.5 - Distance Formula 9.5/1-14

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