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 look at how to find the length of a line segment algebraically when we're given information and measurements near parts of the line segment.

Call back that a line segment is a finite piece of a line, named by its endpoints. For case, the line segment ???\overline{AB}??? might await like this:

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line segment named by its endpoints

Line segments and distance

The distance between ii points on a line segment is called the length of the segment. Nosotros unremarkably utilise the same symbol for the length of the line segment that we apply for the segment itself. Then ???\overline{AB}??? could exist used to represent the segment itself, but also the length of the segment.

line segment on a number line

In this case, the distance betwixt points ???A??? and ???B??? is

???\overline{AB}=|iii-(-2)|???

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

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

???\overline{AB}=v???

In this example, y'all could besides count from ???A??? to ???B??? and become a distance of ???5???. As you tin run into, sometimes information technology may be helpful to draw a number line in order to visualize the length of a line segment.

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

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Using a number line to solve midpoint problems

Case

Points ???Due south???, ???T???, ???U???, ???Five???, and ???W??? prevarication in club on a number line. Signal ???U??? is at ???-2???. Where are the residual of the points located?

???\overline{ST}=2???

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

???\overline{UV}=iii???

???\overline{VW}=2???

If nosotros plot point ???U??? at ???-2???, and then ???S???, ???T???, ???U???, ???V???, and ???West??? must be plotted this way:

plotting points on a number line

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

Let's look at some other example.

Length of a line segment for Geometry

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

Instance

Notice ???\overline{AB}???, if ???\overline{Air conditioning}=12??? and ???\overline{BC}=vii???.

finding length of a line segment

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

We tin can see that ???\overline{AC}-\overline{BC}=\overline{AB}???, and then we have ???\overline{AB}=12-7=5???.

Let's look at one terminal example.

Example

The locations of four points on a number line are ???A=2???, ???B=4???, ???C=-3???, and ???D=-half-dozen???. What is the value of ???\overline{AB}+\overline{CD}????

Nosotros can draw a number line to aid solve the problem.

plotting four points on a number line

Now we tin can run across that ???\overline{AB}=|4-2|=two??? units and ???\overline{CD}=|-three-(-6)|=3??? units. So ???\overline{AB}+\overline{CD}=2 + 3 = 5??? units.

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