2. The Distance Formula Produced by Kevin Horace Mann Middle School Ms. Wiltshire’s Class

3. 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

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

5. PYTHAGOREAN THEOREM /DISTANCE FORMULA PYTHAGOREAN THEOREM DISTANCE FORMULA

6. USING THE PYTHAGOREAN THEOREM NASA MAP

7. COMPUTATION THE CHANGE IN LATITUDE IS 5 DEGREES (117-122) THE CHANGE IN LONGITUDE IS 3 DEGREES (37-34) THESE DISTANCES ARE THE LEGS OF THE RIGHT TRIANGLE.

8. USING THE DISTANCE FORMULA NASA MAP

9. COMPUTATION NASA DRYDEN IS LOCATED AT 117 DEGREES LONGITUDE AND 34 DEGREES LATITUDE. NASA AMES IS LOCATED AT 122 DEGREES LONGITUDE AND 37 DEGREES LATITUDE. CONSIDER EACH LOCATION A COORDINATE PAIR (34,117) AND (37,122)

10. DISTANCE FORMULA

11. WHAT DID WE LEARN? HOW TO COMPUTE DISTANCE USING THE PYTHAGOREAN THEOREM AND THE DISTANCE FORMULA HOW TO USE LATITUDE AND LONGITUDE WHAT DEGREES ARE

12. SO, HOW FAR IS IT REALLY? ONE DEGREE EQUALS ABOUT 60 NAUTICAL MILES 5.83 DEGREES EQUALS 349.8 NAUTICAL MILES (5.83*60)

13. NOW WE CAN COMPUTE THE DISTANCE BETWEEN ANY TWO CITIES,PLACES,OR GEOGRAPHICAL FEATURES BY USING A MAP WITH LATITUDE AND LONGITUDE.

14. VOCABULARY DEGREE LATITUDE LONGITUDE HYPOTENUSE COORDINATE THEOREM

15. CREDITS CYNTHIA LANIUS-MATHEMATICS OF CARTOGRAPHY ROBIN A. WARD-LATITUDE AND LONGITUDE A REAL LIFE EXAMPLE NASA

16. THE END