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Distance And Midpoint

Distance And Midpoint. Section 1-3. Spi.2.1.E. Jim Smith JCHS. The distance between 2 points is the absolute value of the difference of the coordinates . The distance between exit 417 and 407 is | 417 – 407 | = 10 or | 407 – 417 | = | -10 | = 10. A B.

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Distance And Midpoint

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  1. Distance And Midpoint Section 1-3 Spi.2.1.E Jim Smith JCHS

  2. The distance between 2 points is the absolute value of the difference of the coordinates. The distance between exit 417 and 407 is | 417 – 407 | = 10 or | 407 – 417 | = | -10 | = 10

  3. A B | | | | | | | | | | | | | | -5 4 The distance between A and B is | -5 – 4 | = | -9 | = 9 Our distances should always be positive

  4. A B | | | | | | | | | | | | | | -6 12 The midpoint of a segment is the average of the coordinates 6 2 -6 + 12 2 = 3 =

  5. Review Graphing y Order ( X,Y ) Positive x ( 0,0 ) Origin Negative

  6. The Distance Formula Is Derived From The Pythagorean Formula A B

  7. Dist = ( x - x )² + ( y - y )² Distance Formula Remember the order ( x , y ) Check yourself … our answers should be positive

  8. ( 8 – 3 )² + ( 10 – 6 )² ( 5 )² + ( 4 )² 25 + 16 41 =6.40 Find the distance between: ( 3 , 6 ) and ( 8 , 10 ) ( 3 – 8 )² + ( 6 - 10 )² ( -5 )² + ( -4 )² 25 + 16 41 = 6.40

  9. MIDPOINT The midpoint of a segment is half way between the x’s and half way between the y’s You can call it the average Midpoint 6 10

  10. Midpoint Formula X + X , Y + Y 2 2 Find the midpoint of ( 2,8 ) and ( 6,4 ) 2 + 6 , 8 + 4 = 8 ,12 = ( 4 , 6 ) 2 2 2 2

  11. X1 + X2 2 =XMID Y1 + Y2 2 = YMID What If We Knew The Midpoint Of A Segment And One Endpoint? How Would We Find The Other Endpoint? Think Of The Formula As: Endpoints Midpoint (X1 , Y1)(X2 , Y2)( Xmid , Ymid)

  12. X1 + X2 2 Y1 + Y2 2 =XMID = YMID Endpoint ( 3 , 5 ) Midpoint ( 6 , -2 ) Find The Other Endpoint. Find ( X2 ,Y2 ) 5 + Y2 2 5 + Y2 Y2 = -9 3 + X2 2 3 + X2 X2 = 9 = -2 = 6 = -4 = 12 ( 9 , -9 )

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