Midpoint
Formula
Midpoint formula
Finding the distances between any 2 points is a very critical topic in geometry!
The formula, as you may recall, is the following:
( x₂ - x₁ )² + (y₂ - y₁)²
The two points that we are trying to find the distance of are (x1, y1) and (x2, y2) and the formula utilizes
the Pythagorean theorem to find the shortest distance between those two points. But what if we wanted
to find the midpoint of those two points?
There is a much simpler formula for this, and it is called the midpoint formula
Midpoint X val Midpoint y val
x₁ + x ₂ y₁ + y ₂
2 2
Example A
If you are given two points, you need to find the middle value for the x coordinate, the middle value for
the y coordinate, and then combine them to get the midpoint coordinate pair. Let’s work through an
example:
Let’s say you had the two points (2, 3) and (5, 7). What would the midpoint be?
Let’s start out with the x value:
● Add the 2 x values → 2+5=7. Then you divide 7/2 to get 3.5. This is the x value
Example A
Let’s do the y value midpoint next
● When we add up 3+7=10. When we
divide 10/2, we get 5.
● Combine the x and y values to get (3.5, 5).
Let’s plot all 3 points on a graph to check
that (3.5, 5) is indeed the midpoint
● It is! The distances are the same from
the midpoint to the 2 points we started
with
Example B
Let’s say you had the two points (3, 15) and (12, 9). What would the midpoint be?
Let’s start out with the x value
● Add the 2 x values → 3+12=15. Then divide 15/2 to get 7.5. That’s the x value
Let’s do the y value midpoint next
● 15+9=24. When divide 24/2, we get 12, which is the midpoint y value.
● (7.5, 12) is our midpoint coordinate, at an equal distance from both points
Thanks!
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