Distance And Midpoint Section 1-5

OBJECTIVES SWBAT: Find the distance between two points on the coordinate system Find the coordinate of the midpoint

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

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

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

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

The Distance Formula Is Derived From The Pythagorean Formula B

our answers should be positive Distance Formula Remember the order ( x , y ) Check yourself … our answers should be positive

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

MIDPOINT 6 10 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

Midpoint Formula Find the midpoint of ( 2,8 ) and ( 6,4 )

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

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