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# 1 3 distance and midpoint

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### 1 3 distance and midpoint

1. 1. Distance And Midpoint Section 1-3 Jim Smith JCHS Spi.2.1.E
2. 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. 3. The distance between A and B is | -5 – 4 | = | -9 | = 9 Our distances should always be positive | | | | | | | | | | | | | | -5 4 A B
4. 4. The midpoint of a segment is the average of the coordinates -6 + 12 2 = 6 2 = 3 | | | | | | | | | | | | | | -6 12 A B
5. 5. Review Graphing y x ( 0,0 ) Origin Positive Negative Order ( X,Y )
6. 6. A B The Distance Formula Is Derived From The Pythagorean Formula 6 15 6 ² + 15² = AB² √ 261
7. 7. Distance Formula Remember the order ( x , y ) Check yourself … our answers should be positive Dist = ( x - x ) ² + ( y - y )²
8. 8. Find the distance between: ( 3 – 8 ) ² + ( 6 - 10 )² ( -5 )² + ( -4 )² 25 + 16 41 = 6.40 ( 3 , 6 ) and ( 8 , 10 ) ( 8 – 3 ) ² + ( 10 – 6 )² ( 5 )² + ( 4 )² 25 + 16 41 =6.40
9. 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 6 10 Midpoint
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. 11. 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 ( X 1 , Y 1 ) ( X 2 , Y 2 ) ( X mid , Y mid ) X 1 + X 2 2 = X MID Y 1 + Y 2 2 = Y MID
12. 12. Endpoint ( 3 , 5 ) Midpoint ( 6 , -2 ) Find The Other Endpoint. Find ( X 2 , Y 2 ) 3 + X 2 2 3 + X 2 X 2 = 9 = 6 = 12 5 + Y 2 2 5 + Y 2 Y 2 = -9 = -2 = -4 ( 9 , -9 ) X 1 + X 2 2 = X MID Y 1 + Y 2 2 = Y MID