3. For lines that are vertical (x,y) or horizontal (x,y) the length is easy to find (-5, 9) R V ( -5, -7) All you have to do is subtract the y-coordinates to find my length M (-2, 3) E ( 7, 3) All you have to do to find me is subtract the x-coordinates

4. To find the length of a nonvertical or nonhorizontal the distance formula is to be used: A (-2,2) B (3,-3) x 1 and x 2 are the x-coordinates of A and B (it doesn’t matter which one is x 1 and which one is x 2 so it could be –2–3 or 3–(-2)) y 1 and y 2 are the y-coordinates of A and B (it doesn’t matter which one is y 1 and which one is y 2 so it could be 2–(-3) or (-3)–2)

5. Here are some helpful examples: M R (-3,9) (2,-2) Find the length of MRFind the length of CD C D (-3,-8) (1,8) (x 1 -x 2 ) + (y 1 -y 2 ) 22 (-3-2) + (9+2) 22 (-5) + (11) 22 25 + 121 146 MR =146 (x 1 -x 2 ) + (y 1 -y 2 ) 22 (-3-1) + (-8-8) 22 (-4) + (-16) 22 16 + 256 272 1617 CD = 417

6. Now you try: G K (1,4) (4,0) 1.) Find GK L M 2.) Find LM (-2,1) (1,-4) N O (-1,2) (0,-3) 3.) Find NO X Y (-3,5) (4,-5) 4.) Find XY

7. Answers 1.) (4-1) + (4-0) 22 3 + 4 22 9 + 16 25 GK = 5 2.) (1 + 2) + (1 + 4) 22 (3) + (5) 22 9 + 25 34 LM = 3.) (0 + 1) + (2 + 3) 22 1 + 5 22 1 + 25 26NO = 4.) (4 + 3) + ( 5 + 5) 22 7 + 10 22 49 + 100 149 XY =

8. Can You Do This? R A Y (-3,-7) (-3,11) (6,-7) Find the perimeter of triangle RAY

9. Answer First find RA and RY RA = 11–(-7) RY = 6-(-3) RA = 18 RY = 9 Now find AY using the distance formula (6 + 3) + (11 + 7) 22 9 + 18 22 81 + 324 405 815 59 Now to find the perimeter add all the lengths together: 9 + 18 + 9 The perimeter is: 27 + 9 5 5

10. Fun Facts Did you know the distance formula came from the Pythagorean therom? http://www.mathwarehouse.com/algebra/distance_for mula/interactive-distance-formula.php This site lets you drag around the points and see the distance formula at workhttp://www.mathwarehouse.com/algebra/distance_for mula/interactive-distance-formula.php Some fun practice http://www.regentsprep.org/Regents/Math/distance/Pr acDistance.htm http://www.regentsprep.org/Regents/Math/distance/Pr acDistance.htm

11. Works Cited “Interactive Distance Formula” Math Ware House.. 29 May 2008 Rhoad, Richard, George Milauskas, and Robert Whipple. Geometry for Enjoyment and Challenge. Boston: McDougal Little, 1991 Stapel, Elizabeth. "The Distance Formula.“ Purplemath.. 29 May 2008 “Working With Distance.” 1999-2008. Oswego City School District Regents Exam Prep Center.. 29 May 2008.