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Midpoint Formula
Coordinate Geometry • Grades 8, 9, 10
Coordinate Geometry
Midpoint Formula
Calculate the exact center point between any two coordinates on the Cartesian plane.
The Formula
M = ((x₁+x₂)/2, (y₁+y₂)/2)
Used for: Finding the exact center coordinates between two endpoints on the Cartesian coordinate plane
MMidpoint coordinates (x_m, y_m)
(x₁, y₁)Coordinates of first endpoint
(x₂, y₂)Coordinates of second endpoint
⚡Live Interactive Quick Solver
Instant CalculationMidpoint (M):(2.50, 4.00)
Step: M = ((1 + 4)/2, (2 + 6)/2) = (2.5, 4)
M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
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🎯 Key Concepts & Rules
Essential principles for calculating with this formula:
📍
Average of x and yAdd the coordinates and divide each by 2: M = ((x₁+x₂)/2, (y₁+y₂)/2).
📏
EquidistantThe midpoint divides the line segment into two equal halves.
📝 Worked Examples & Step-by-Step Solutions
Example 1: P₁(2, 4) and P₂(8, 10)
Problem:
Find the midpoint between (2, 4) and (8, 10).1
x-coordinate
x_m = (2 + 8) / 2 = 10 / 2 = 52
y-coordinate
y_m = (4 + 10) / 2 = 14 / 2 = 7Answer: M = (5, 7)
💡 Pro Tips & Common Mistakes
Finding Missing Endpoint
If you know one endpoint and the midpoint, use x₂ = 2x_m - x₁.
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