CK-12 Geometry-Concepts

http://www.ck12.org Chapter 1. Basics of Geometry

Example A

IsMa midpoint ofAB?

No, it is not becauseMB=16 andAM= 34 − 16 =18.

Example B

Find the midpoint between (9, -2) and (-5, 14).

Plug the points into the formula.

(

9 +(− 5 )

2

,

− 2 + 14

2

)

=

(

4

2

,

12

2

)

= ( 2 , 6 )

Example C

IfM( 3 ,− 1 )is the midpoint ofABandB( 7 ,− 6 ), findA.

Plug what you know into the midpoint formula.

(

7 +xA

2

,

− 6 +yA

2

)

= ( 3 ,− 1 )

7 +xA

2

=3 and

− 6 +yA

2

=− 1 Ais(− 1 , 4 ).

7 +xA=6 and− 6 +yA=− 2

xA=−1 andyA= 4

Another way to find the other endpoint is to find the difference betweenMandBand then duplicate it on the other
side ofM.

x−values: 7− 3 =4, so 4 on the other side of 3 is 3− 4 =− 1

y−values:− 6 −(− 1 ) =−5, so -5 on the other side of -1 is− 1 −(− 5 ) = 4

Ais still (-1, 4). You may use either method.

Example D

Use a ruler to draw a bisector of the segment below.