The Distance and Midpoint Formulas

Goal 1 Find the Midpoint of a Segment

Goal 2 Find the distance between two points on a coordinate plane

Goal 3 Find the slope of a line between two points on a coordinate plane

Distance Formula Used to find the distance between two

points

2 22 1 2 1distance ( ) ( )x x y y

),(),( 2211 yxandyx

Example Find the distance between (2,1) and (5,2).

D= (2 - 5)² + (1 - 2)² D= (-3)² + (-1)² D= 9+1 D= 10 D= 3.162

x1 y1 x2 y2

-First substitute numbers for variables and solve the parentheses.-Then solve the squared number.

-Add the two numbers.

-Find the square root of the remaining number.

Example Find the distance between A(4,8) and

B(1,12)

2 22 1 2 1distance ( ) ( )x x y y

A (4, 8)

B (1, 12)

2 2distance (1 4) (12 8) 2 2distance ( 3) (4)

distance 9 16 25 5

),(),( 2211 yxandyx

YOU TRY!! Find the distance between:

A. (2, 7) and (11, 9)

B. (-5, 8) and (2, - 4)

2 2(9) (2) 85

2 2(7) ( 12) 193

Midpoint Formula Used to find the center of a line

segment

2 1 2 1midpoint ,2 2

x x y y

),(),( 2211 yxandyx

Example Find the midpoint between A(4,8) and

B(1,12)

2 1 2 1midpoint ,2 2

x x y y

A (4, 8)

B (1, 12)

1 4 12 8midpoint ,2 2

midpoint 5 ,102

YOU TRY!! Find the midpoint between: A) (2, 7) and (14, 9)

B) (-5, 8) and (2, - 4)

midpoint = 8,8

-3midpoint = , 22

THE SLOPE FORMULA!

12

12

xxyym

( -5, -3)

(6, 5)

Use the slope formula

6553

= 118

= 118

12

12

xxyy

2x

1x 1y

2y

Classwork Complete the handout given in

class.

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