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The 90 mile straight section of highway lies between the towns of Balladonia and Caiguna in the Australian Outback.
Some friends of ours recently drove this stretch of the Eyre Highway.
If their car started making some strange noises along this section of road, would they be better off heading back to Balladonia, or continuing onto Caiguna?
Well assuming there is a mechanic in each town, it would depend on whether they had crossed the halfway point, (or “Midpoint”), of their journey.
Eg. If they had not passed the halfway midpoint, then they are better off heading back to Balladonia, because it is less distance to drive with a dodgy sounding engine.
This lesson is all about finding midpoints on straight lines.
Finding the Midpoint along the “90 mile Straight” is fairly simple.
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Finding the Midpoint Between Two Points
To find the Midpoint Between any two (x,y) coordinates, we simply add the x coordinates and divide by 2, and also add the y-coordinates and divide by 2.
Here is an example where we have worked out the Midpoint manually.
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Try the following example, and see how you go.
(The answer is further down this web page).
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Here is the answer to the above Example Question.
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Practical Application of Midpoint
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If a plane flying between two cities gets some engine damage, it would need to be determined from the Coordinates in the GPS Navigation system, if the plane is less than halfway through its flight distance or not.
A decision can then be made either to turn back, or keep flying to the final destination.
The Pilots are not going to get out graph paper and count squares to work out where they are !
Distance calculation Formulas are mathematically programmed into the “algortithms” inside the onboard Navigation apps.
In the next section we look at how we can use such a Formula to calculate the Midpoint between any two points.
Midpoint Formula
The following is the Midpoint Formula for two points.
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Here is a quick three and a half minute video about how the Midpoint Formula is used.
Midpoint Formula – Working Out Steps
To obtain the Midpoint we follow these steps:
Step 1 – Label our two points (x1, y1) and (x2,y2)
Step 2 – Get the average of the x values, then get the average of the y values
Step 3 – Simplify our x and y answers and write them as an (x,y) coordinate.
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More Midpoint Videos
The following video shows how to sketch two points and do a Midpoint Formula Calculation
Here is a video which shows how to do the Midpoint when the coordinates are fractions.
This video goes into a fair amount of detail, and shows an example where you are given the Midpoint, and have to work backwards to find one of the end points.
Midpoint Calculation Examples
Finish off Example 1 shown below, and find the Midpoint.
(The solution answer is shown further down the page)
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Here is the fully worked solution to Example 1.
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Finish off Example 2 shown below, and find the Midpoint.
(The solution answer is shown further down the page)
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Here is the fully worked solution to Example 2.
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Midpoint – Alternative Working Out
If you are struggling with using the Algebra Formula, or you simply want to quickly check an answer, then try this alternative working out method.
Line up the two points under each other and then add them up to get an answer point.
Divide this answer point by 2 to get the final Midpoint Answer Point.
Here are out two previous examples done the alternative way.
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Midpoint Calculators
This first calculator provides DECIMAL Answers.
Note that we have to click the right scroll down arrow to get to the final answer.
Click the following link to access this calculator.
http://ncalculators.com/geometry/mid-points-calculator.htm
This second calculator provides FRACTION Answers.
Note that we have to go down the webpage to get to the calculator.
Click the following link to access this calculator.
http://www.mathwarehouse.com/geometry/midpoint-calculator.php
Midpoint Songs
Here is a quick 16 second Cheerleader “Cheer” to help remember the Midpoint Process.
This garage acoustic rock song severely lacks studio production and smooth vocals, but the message is there.
Midpoint Worksheets
This first worksheet has a set of Basic Midpoint Questions with answers on the second page.
There are plenty of questions with answers on this second worksheet.
It includes Line Graphs as well as working backwards end point questions.
Related Items
The Cartesian Plane
Plotting Graphs from Horizontal Values Tables
Plotting a Linear Graph using a Rule Equation
Plotting Graphs from T-Tables of Values
Finding Linear Rules
Distance Between Two Points
Gradient and Slope
Mountain Gradients
Real World Straight Line Graphs I
Real World Straight Line Graphs II
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