Finding length and midpoint of a line segment

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What is the midpoint of a line segment?

In this lesson nosotros'll look at how to discover the length of a line segment algebraically when we're given information and measurements about parts of the line segment.

Call back that a line segment is a finite piece of a line, named past its endpoints. For instance, the line segment ???\overline{AB}??? might expect similar this:

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line segment named by its endpoints

Line segments and altitude

The altitude between 2 points on a line segment is chosen the length of the segment. We usually use the same symbol for the length of the line segment that we utilise for the segment itself. So ???\overline{AB}??? could be used to represent the segment itself, only also the length of the segment.

line segment on a number line

In this example, the distance between points ???A??? and ???B??? is

???\overline{AB}=|3-(-ii)|???

???\overline{AB}=|3+2|???

???\overline{AB}=|5|???

???\overline{AB}=5???

In this instance, you could also count from ???A??? to ???B??? and get a distance of ???5???. As yous tin can see, sometimes it may exist helpful to describe a number line in lodge to visualize the length of a line segment.

Finding the length of a line segment, and and then its midpoint

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Using a number line to solve midpoint problems

Instance

Points ???S???, ???T???, ???U???, ???V???, and ???W??? prevarication in order on a number line. Point ???U??? is at ???-2???. Where are the remainder of the points located?

???\overline{ST}=two???

???\overline{TU}=1???

???\overline{UV}=3???

???\overline{VW}=two???

If we plot bespeak ???U??? at ???-2???, then ???Southward???, ???T???, ???U???, ???5???, and ???W??? must be plotted this way:

plotting points on a number line

We know indicate ???U??? is on ???-ii??? and ???\overline{TU}=1???. This lets the states locate signal ???T??? at ???-three???. Now we tin use ???\overline{ST}=2??? to find that ???S=-5??? and ???\overline{UV}=3??? to find that ???Five=1???. At present we can locate point ???W??? by using ???\overline{VW}=two???, so ???Westward=3???.

Let'due south wait at some other example.

Length of a line segment for Geometry

The distance between two points on a line segment is called the length of the segment.

Example

Notice ???\overline{AB}???, if ???\overline{AC}=12??? and ???\overline{BC}=7???.

finding length of a line segment

We know that ???\overline{AC}=12??? and ???\overline{BC}=7???. From the diagram, we also know that ???\overline{AB}??? is role of ???\overline{AC}???.

We can see that ???\overline{AC}-\overline{BC}=\overline{AB}???, so we take ???\overline{AB}=12-seven=5???.

Allow's look at one last instance.

Example

The locations of iv points on a number line are ???A=2???, ???B=iv???, ???C=-3???, and ???D=-6???. What is the value of ???\overline{AB}+\overline{CD}????

We tin can draw a number line to help solve the problem.

plotting four points on a number line

Now we can see that ???\overline{AB}=|four-2|=2??? units and ???\overline{CD}=|-three-(-6)|=3??? units. So ???\overline{AB}+\overline{CD}=2 + 3 = 5??? units.

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