CK-12 Geometry Concepts

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

(

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.

The first step in identifying a bisector is finding the midpoint. Measure the line segment and it is 4 cm long. To find
the midpoint, divide 4 by 2.

So, the midpoint will be 2 cm from either endpoint, or halfway between. Measure 2 cm from one endpoint and draw
the midpoint.

To finish, draw a line that passes through the midpoint. It doesn’t matter how the line intersectsXY, as long as it
passes throughZ.

Watch this video for help with the Examples above.

MEDIA

Click image to the left for more content.

CK-12 Foundation: Chapter1MidpointsandSegmentBisectorsB

Vocabulary

Amidpointis a point on a line segment that divides it into two congruent segments. A line, segment, or ray that
passes through a midpoint of another segment is called asegment bisector. When the bisector intersects the segment
at a right angle, it is called aperpendicular bisector.