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The Distance Formula

The Distance Formula. Finding The Distance Between Points. On maps and other grids, you often need to find the distance between two points not on the same grid line. This is used for: Taking a car trip Flying a plane Targeting a rocket Computing the distance a football is thrown.

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The Distance Formula

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  1. The Distance Formula

  2. Finding The Distance Between Points • On maps and other grids, you often need to find the distance between two points not on the same grid line. • This is used for: • Taking a car trip • Flying a plane • Targeting a rocket • Computing the distance a football is thrown

  3. Investigating Distance • Plot A (0,0) and B (4,5) on graph paper. Then draw a right triangle that has the line segment AB as its hypotenuse. • Label the coordinates of the vertices. • Find the length of the legs of the right triangle. • Use the Pythagorean Theorem to find the length of the hypotenuse.

  4. complete the sample problem in your INB

  5. Complete the next two on your own

  6. Steps to finding distance on the coordinate grid using the Pythagorean Theorem • Graph the points on the coordinate plane, if needed • Draw a right triangle, with the hypotenuse connecting the two points. • Count vertically for the 1st leg length • Count horizontally for the 2nd leg length. • Use the Pythagorean Theorem to find the hypotenuse and therefore the distance between the two points.

  7. Assignment for Today • Complete worksheet on finding distance between two points using the Pythagorean Theorem

  8. Review of finding distance on the coordinate plane

  9. Finding distance on the coordinate plane Without directly using the Pythagorean Formula

  10. Finding distance on a map Find the distance from the corner of Avenue 2 and 1st Street (A) to the corner of Avenue 4 and 6th Street.

  11. Steps for finding distance

  12. Your turn

  13. Steps to solving for distance

  14. Example 1 • Find the distance between the points A (3, 7) and B (8, 2)

  15. Example 2 • Find the distance between the points (3,-6) and (-9,0)

  16. Example 3 • Find the distance between the two points (8,-8) and the origin

  17. Assignment • Complete the worksheet

  18. Applications of Distance Formula

  19. USING THE PYTHAGOREAN THEOREM • NASA MAP

  20. USING THE DISTANCE FORMULA • NASA MAP

  21. Another example • If a building is located on a city map at (2,6) and the park is located at (2,0). Find the distance between the building and the park.

  22. Final Example • On the galactic grid, a quasar is located at (54, 29). A black hole is located at (32, 15). How far is the quasar from the black hole.

  23. DISTANCE FORMULA

  24. WHAT DID WE LEARN? • HOW TO COMPUTE DISTANCE USING THE PYTHAGOREAN THEOREM AND THE DISTANCE FORMULA • How to find distances from a map

  25. THE END

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