Midpoint Formula — SAT Math Explained
A formula that finds the exact middle point between two given points in the coordinate plane: Midpoint = ((x₁ + x₂)/2, (y₁ + y₂)/2).
The Core Idea
The midpoint is simply the average of the x-coordinates and the average of the y-coordinates. Averaging finds the middle of any two values — this extends naturally to 2D.
Step-by-Step: How to Approach Midpoint Formula
Identify the coordinates of both endpoints
Add the x-coordinates and divide by 2 → this is the x-coordinate of the midpoint
Add the y-coordinates and divide by 2 → this is the y-coordinate of the midpoint
Write the midpoint as an ordered pair (x, y)
Applications
Finding the center of a line segment
Finding the center of a circle given the endpoints of its diameter
Verifying that a point bisects a segment
Working Backwards
If given one endpoint and the midpoint, find the other endpoint: if (x₁, y₁) is one endpoint and (mx, my) is the midpoint, then x₂ = 2mx - x₁ and y₂ = 2my - y₁
Common Errors to Avoid
Subtracting coordinates instead of adding (that would give half the distance, not the midpoint coordinates)
Forgetting to divide by 2
Confusing midpoint formula with distance formula
Practice: Midpoint Formula
5 SAT-style questions. Select your answer and get an instant explanation.
Midpoint of (0,0) and (8,6)?
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