What is the Midpoint Formula?
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Definition: The midpoint formula, in geometry, is an equation that calculates the halfway point distance between two known coordinate points.
In economics, the midpoint formula is used to measure changes in supply and demand curves and their relative elasticity.
Midpoint Formula Uses
The midpoint formula is often used to find the midpoint in order to bisect a line segment. It can also be used to prove that a line segment is bisected.
The formula is finding the average, or median of two values. This formula is often utilized with maps and with the distance formula.
For example, Find the city that is between Chicago, Illinois and Indianapolis, Indiana. How far is the city from Chicago?
To answer this question, let’s see how to find the midpoint below.
What is the Midpoint of a Line?
A midpoint is a coordinate point that is halfway between two other points on a line segment.
Midpoints occur in both two dimensional space on a graph and three dimensional space inside of a cube, sphere, or other shape.
Finding the midpoint helps calculate geographical, computer programing, and economic problems.
Let’s see how to calculate this equation.
Distance & Midpoint Formula Equation
The midpoint formula equation is calculated by adding two coordinate points ( x1, y2 ) and ( x2, y2 ) and dividing by two. The midpoint, represented by M, is calculated by the following:
The subscripts, the small numbers at the base of the variables are referencing the point from which the value is coming from. Since the formula uses addition, and order doesn’t affect the sum, the order in which you add the values is not important.
What is important is to make sure that you are adding the x-coordinates together and adding the y-coordinates together. Also take note that the answer is in the form of a coordinate, since the midpoint is a point, the solution should also be in coordinate form.
Midpoint Formula Examples In Geometry
Midpoint of a Straight Line Segment Example
The midpoint of a line segment formula will calculated the mid point of that segment. When solving each variable, be sure to add then divide by two.
When the line segment is vertical or horizontal, one of the coordinates does not change.
First we will label our variables with the subscripts one or two.
Next we will substitute the values into the formula.
Add the values in the numerator.
Simplify the fractions. If the numerator is odd, often time the result is left in decimal form, but a mixed or improper fraction is acceptable as well.
Notice that for the horizontal line, the y-coordinate of the midpoint is the same as both end points. The vertical line midpoint has the same x-coordinate as the end points.
This can help save time on solving the problem, however if you tend to mix up the x and y-coordinates, then it may be best to complete each step to avoid errors.
Midpoint of a Diagonal Line Example
Let’s look at a midpoint formula geometry example where the line segment is diagonally positioned.
First we need to find the coordinates of the points.
We will make point A our first point (subscript 1) and point B our second point (subscript 2)
Next we will substitute the values into the formula and simplify.
Midpoint Method Formula in Economics
Midpoint Method Formula Example
The midpoint method is often used in Economics to measure the price elasticity of demand and supply curve changes and the economic impact of each.
Economics uses the midpoint formula method of slope and apply it to triangles.
Another type of problem that would use midpoints is finding the second endpoint of a segment.
Given a line segment that has an endpoint of (-3,-5) and has a midpoint at (1,1), find the other endpoint of the line segment.
One way that we can solve this is to use the midpoint formula. We can break it down to look at the x-coordinates and y-coordinates separately.
We will start by labeling our known endpoint as while our midpoint is . Now we can substitute in our known values.
Start by multiplying both sides by 2. This will cancel out the fraction.
Subtract, or in this case add since we have a negative value, in order to isolate the variable.
The coordinates of the second endpoint is (5,7).
Midpoint Formula Economics Example
A second way to find the missing endpoint in the midpoint formula economics is to use slope. We will explore this method using the same values.
Let’s start by sketching out a diagram.
Let’s find the slope between the endpoint and the midpoint.
The slope is 6/4 . We are not going to reduce the slope since we want the same values. The 6 represents the vertical change, or the change in the y-coordinate.
This means we can add 6 to the y-coordinate of our midpoint. The 4 represents the horizontal change, or the change in the x-coordinate. We can add 4 to our x-coordinate of our midpoint. This gives us the coordinates of the second endpoint (5,7).