Finding length and midpoint of a line segment

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What is the midpoint of a line segment?

In this lesson we'll await at how to detect the length of a line segment algebraically when we're given data and measurements about parts of the line segment.

Retrieve that a line segment is a finite piece of a line, named by its endpoints. For instance, the line segment ???\overline{AB}??? might wait similar this:

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line segment named by its endpoints

Line segments and distance

The altitude betwixt two points on a line segment is chosen the length of the segment. We usually use the aforementioned symbol for the length of the line segment that we use for the segment itself. So ???\overline{AB}??? could be used to represent the segment itself, just also the length of the segment.

line segment on a number line

In this instance, the altitude between points ???A??? and ???B??? is

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

???\overline{AB}=|iii+ii|???

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

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

In this case, you could as well count from ???A??? to ???B??? and become a distance of ???5???. Equally you lot tin can meet, sometimes information technology may be helpful to depict a number line in order to visualize the length of a line segment.

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

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Using a number line to solve midpoint bug

Example

Points ???South???, ???T???, ???U???, ???V???, and ???Westward??? prevarication in guild on a number line. Point ???U??? is at ???-two???. Where are the balance of the points located?

???\overline{ST}=ii???

???\overline{TU}=i???

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

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

If we plot indicate ???U??? at ???-2???, then ???S???, ???T???, ???U???, ???5???, and ???West??? must be plotted this way:

plotting points on a number line

Nosotros know point ???U??? is on ???-ii??? and ???\overline{TU}=1???. This lets united states locate bespeak ???T??? at ???-three???. Now we tin can utilize ???\overline{ST}=ii??? to detect that ???S=-v??? and ???\overline{UV}=3??? to find that ???V=1???. Now we can locate betoken ???W??? by using ???\overline{VW}=2???, and so ???West=3???.

Allow's look at another example.

Length of a line segment for Geometry

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

Example

Find ???\overline{AB}???, if ???\overline{Air conditioning}=12??? and ???\overline{BC}=7???.

finding length of a line segment

Nosotros know that ???\overline{Air-conditioning}=12??? and ???\overline{BC}=7???. From the diagram, we likewise know that ???\overline{AB}??? is part of ???\overline{Ac}???.

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

Let's await at ane last example.

Example

The locations of iv points on a number line are ???A=2???, ???B=4???, ???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 trouble.

plotting four points on a number line

Now nosotros can run into that ???\overline{AB}=|4-2|=2??? units and ???\overline{CD}=|-3-(-vi)|=3??? units. So ???\overline{AB}+\overline{CD}=2 + 3 = v??? units.

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