CK-12 Geometry - Second Edition

1.4. Midpoints and Bisectors http://www.ck12.org

Let’s create a formula from this. If the two endpoints are (-5, 6) and (3, 4), then the midpoint is (-1, 4). -1 ishalfway
between -5 and 3 and 4 ishalfwaybetween 6 and 2. Therefore, the formula for the midpoint is the average of the
x−values and the average of they−values.

Midpoint Formula:For two points,(x 1 ,y 1 )and(x 2 ,y 2 ), the midpoint is

(x 1 +x 2

2 ,

y 1 +y 2

2

)

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

Solution:Plug the points into the formula.

(

9 +(− 5 )

2

,

− 2 + 14

2

)

=

(

4

2

,

12

2

)

= ( 2 , 6 )

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

Solution: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.

Segment Bisectors

Segment Bisector:A line, segment, or ray that passes through a midpoint of another segment.

A bisector cuts a line segment into two congruent parts.

Example 4:Use a ruler to draw a bisector of the segment below.