Let’s learn how to find the midpoint using the midpoint formula.
What is a Midpoint?
A line segment’s midpoint refers to the middle point that divides it into two equal parts. Finding the midpoint between two numbers simply means finding the average of those two numbers. For instance, if you have a line with endpoints at 2 and 10, its midpoint is 6:
(x1 + x2) / 2
2 + 10 = 12
12 ÷ 2 = 6
Using the Midpoint Formula in a Coordinate Plane
The midpoint formula is used to determine the midpoint of the line that bisects two defined points. To find the midpoint (M) between two points, (x1,y1) and (x2,y2), use this formula:
M = [(x1 + x2) / 2, (y1+y2) / 2]
Where M is the Midpoint; x1 and x2 are the x-coordinates; y1 and y2 are the y-coordinates.
Related Reading: Quadratic Formula – Equation & Examples
Example #1: Use the Midpoint Formula to find the Midpoint between (5,5) and (3,-1).
Step 1. Plug the coordinates into the midpoint formula.
M = [(x1 + x2) / 2, (y1+y2) / 2]
=[(5 + 3) / 2, (5 + (-1)) /2]
Step 2. Perform the needed operations, starting with addition.
=[(8 / 2), (4 / 2)]
Step 3. Simplify fractions.
M = (4,2)
Therefore, the midpoint of points (5,5) and (3,-1) is (4, 2).
Here’s the graph of points (5,5) and (3,-1) showing their midpoint (4, 2).
Example #2. If M (2,-1) is the Midpoint of line AB and point A has the coordinates (-4,3), what are the coordinates of point B?
Step 1. Plug the given values into the formula.
M = [(x1 + x2) / 2, (y1+y2) / 2]
M(2,-1)=[(-4 + x2) / 2, (3 + y2) / 2]
Step 2. Find the x-coordinate first using the given midpoint and formula for x.
2 = [(-4 + x2) / 2] Divide both sides by 2.
4 = -4 + x2 Subtract (-4) from both sides.
4 – (-4) = -4 + x2 – (-4)
8 = x2
Step 3. Find the y-coordinate. Do the same steps we did in Step 2.
-1 = [(3 + y2) / 2]
-2 = 3 + y2
-5 = y2
Therefore, the coordinates of B are (8, -5).
Checking the Solution to Example #2:
M = [(x1 + x2) / 2, (y1+y2) / 2]
= [(-4 + 8) / 2, (3 + (-5)) / 2]
= [(4 / 2), ((-2) / 2)]
M = (2, -1)
B(8,-5) is correct.
Here’s the graph of line AB.
Thank you for reading. We hope it’s effective! Always feel free to revisit this page if you ever have any questions about the midpoint formula.
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