Integrated Math 1 / Unit 9: Coordinate Geometry and Constructions
9.2 The Midpoint Formula
Notes
The midpoint of a segment is halfway between its endpoints: $\displaystyle M = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)$.
- It is the average of the $x$-coordinates and the average of the $y$-coordinates.
- Example: midpoint of $(2, 6)$ and $(8, 10)$ is $(5, 8)$.
- To find a missing endpoint: $x_2 = 2x_M - x_1$ and $y_2 = 2y_M - y_1$.
- A midpoint bisects the segment into two equal parts.
Practice
What is the midpoint of the segment with endpoints $(2, 6)$ and $(8, 10)$?
Average the coordinates: $\displaystyle \frac{2 + 8}{2} = 5$ and $\displaystyle \frac{6 + 10}{2} = 8$.
What is the midpoint of the segment with endpoints $(-3, 4)$ and $(5, -10)$?
$\displaystyle \frac{-3 + 5}{2} = 1$ and $\displaystyle \frac{4 + (-10)}{2} = -3$.
The midpoint of segment $AB$ is $(3, 1)$ and $A = (7, -2)$. What is $B$?
$x_B = 2(3) - 7 = -1$ and $y_B = 2(1) - (-2) = 4$.
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