1. Distance And Midpoint
Section 1-5

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

3. 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

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

5. The midpoint of a segment is the average of the coordinates
| | | | | | | | | | | | | |
A B 2 6 2
= 3 =

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

7. The Distance Formula Is Derived From The Pythagorean FormulaB

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

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

10. 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

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

12. 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 )

13. 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 )