lesson 9-6 pages 466-470 the distance and midpoint formulas lesson check 9-5

Lesson 9-6 Pages 466-470

The Distance and Midpoint Formulas

Lesson Check 9-5

What you will learn!1. How to use the Distance

Formula to determine lengths on a coordinate plane.

2. Use the Midpoint Formula to find the midpoint of a line segment on the coordinate plane.

Distance FormulaDistance FormulaMidpointMidpointMidpoint FormulaMidpoint Formula

What you really need to know!

On a coordinate plane, the distance between two points with coordinates (x1 , y1) and (x2 , y2) is given by:

212

212 )()( yyxxd

What you really need to know!

The midpoint of a line segment whose endpoints are (x1 , y1) and (x2 , y2) is given by:

2

)(,

2

)( 2121 yyxx

Example 1:

Find the distance between M(8 , 4) and N(-6 , -2). Round to the nearest tenth, if necessary.

212

212 )()( yyxxd

22 )42()86( d

22 )42()86( d22 )6()14( d

36196d

232d

232d

11727915.2315462d

15.2d

Example 2:

Find the perimeter of ∆XYZ to the nearest tenth.

Side XY: X(-5 , 1), Y(-2 , 4)

212

212 )()( yyxxd

22 )14()52( d22 )3()3( d

18d

Side XZ: X(-5 , 1), Z(-3 , -3)

212

212 )()( yyxxd

22 )13()53( d22 )4()2( d

20d

Side YZ: Y(-2 , 4), Z(-3 , -3)

212

212 )()( yyxxd

22 )43()23( d22 )7()1( d

50d

502018 P

53984315.7858444P

15.8P

Example 3:

Find the coordinates of the midpoint of RS.

2

)( 21 xx

2

)( 21 yy

2

)( 21 xx

2

)( 21 yy

2

)82( 2

)6( 3

2

)24( 2

)6( 3)3,3(

Page 468

Guided Practice

#’s 4-8

Pages 466-468 with someone at home and

study examples!

Read:

Homework: Pages 469-470

#’s 10-30 even

#’s 33-48

Practice Quiz 2 #’s 1-5Lesson Check 9-6

Page

746

Lesson 9-6

Lesson Check 9-6