1 3 Distance and Midpoint The distance from

1. 3 Distance and Midpoint

The distance from point A to point B is 4 units. A B Count spaces not lines.

The distance from point D to point E can be found E with 5 3 c 2 2 2 a +b =c D 4 2 2 2 3 +4 =c 5=c

You can also use the distance formula. E Use ordered (-3, 2) pairs. D (1, -1

The distance between two points (x 1, y 1) and (x 2, y 2) is

(x 1, y 1) y 1 2 a ly 2 -y 1 l y 2 2 c d 2 l lxb -x 2 1 x 1 (x 2, y 2) x 2

Distance formula is based on Pythagorean Theorem. c= √a 2 + 2 b

Find distance between (-3, 2) and ( 1, -1 ) -3 (x 1, y 1) 1 (x 2, y 2) -3 -1 2 ________ d = √( 2 1++3) + ( - 1 - 2 2 )

Find distance between (-3, 2) and ( 1, -1 ) -3 d = √( 1++ d = √( 4 2 3) 2 ) d = √ 16 + 9 d = √ 25 + ( - 1 -2 +(-3 2 )

Find distance between (5, 1) and ( 2, -6 ) (x 1, y 1) ( (x 2, y 2) 2 5) 2 - 5 + ( -6 - 1 2 )

2 5) ( 2 - 5 + ( -6 - 1 d =√ (- 3) 3 2 + (-7 2 ) careful ! d =√ 9 + 49 this is no d =√ 58 = 7. 6 2 -3

2 (-3) = 9 2 -3 is NOT the same Don’t forget the ( ) !!!

The distance from point A to point B is 4 units. A B The MIDPOINT is 1/2 way.

For any 2 points (x 1, y 1) and (x 2, y 2) the midpoint is (x 1, y 1) (x 2, y

Find midpoint (7, 2) and ( -3, 6 ) (x 1, y 1) (x 2, y 2)

(7, 2) and ( -3, 6 ) -3 + 7 , 6 + 2 2 2 4, 8 ( 2, 4) 2 2

Segment AB, has one endpoint A (-1, 5). The midpoint is C( 7, 3). Find the other endpoint B. A C B

Endpoint A (-1, 5). (x 1, y 1) Midpoint C( 7, 3). Find endpoint B. = (7, 3) 5 -1 x 2= 15 y 2= 1 (15, 1)

What kind of triangle is this Find the lengths of the sid 3 = sides is equilateral. 2 = sides is isosceles. no = sides scalene. d d d

The pessimist sees difficulty in every opportunity. The optimist sees the opportunity in every difficulty.