1.2. Distance Between Two Points http://www.ck12.org
Bis betweenAandCin this picture. As long asBisanywhere on the segment, it can be considered to bebetween
the endpoints.
TheSegment Addition Postulatestates that ifA,B, andCare collinear andBis betweenAandC, thenAB+BC=
AC.
The picture above illustrates the Segment Addition Postulate. IfAB= 5 cmandBC= 12 cm, thenACmust equal
5 +12 or 17 cm. You may also think of this as the “sum of the partial lengths, will be equal to the whole length.”
In Algebra, you worked with graphing lines and plotting points in thex−yplane. At this point, you can find the
distances between points plotted in thex−yplane if the lines are horizontal or vertical.If the line is vertical, find
the change in they−coordinates. If the line is horizontal, find the change in thex−coordinates.
Example A
What is the distance marked on the ruler below? The ruler is in centimeters.
Find the absolute value of difference between the numbers shown. The line segment spans from 3 cm to 8 cm.
| 8 − 3 |=| 5 |= 5
The line segment is 5 cm long. Notice that you also could have done| 3 − 8 |=|− 5 |= 5.
Example B
Make a sketch ofOP, whereQis betweenOandP.
DrawOPfirst, then placeQsomewhere along the segment.
Example C
What is the distance between the two points shown below?
Because this line is vertical, look at the change in they−coordinates.
| 9 − 3 |=| 6 |= 6
The distance between the two points is 6 units.
Watch this video for help with the Examples above.
MEDIA
Click image to the left for more content.CK-12 Foundation: Chapter1DistanceBetweenTwoPointsB
Vocabulary
Distanceis the length between two points. Tomeasureis to determine how far apart two geometric objects are.